Researchers Database


FacultyFaculty Division of Natural Sciences Research Group of Mathematics
Last Updated :2022/11/17


Profile and Settings

  • Name (Japanese)

  • Name (Kana)



  • (BLANK), The University of Tokyo

Research Interests

  • パーコレーション、相転移、フラクタル、数理ゲーム

Research Areas

  • Natural sciences, Applied mathematics and statistics
  • Natural sciences, Basic mathematics

Research Experience

  • Apr. 2013, Professor, Division of Natural Sciences, Nara Women's University
  • Apr. 2012, Mar. 2013, Assosiate Professor, Division of Natural Sciences, Nara Women's University
  • Apr. 2007, Mar. 2012, Assosiate Professor, Faculty of Science, Nara Women's University
  • Jul. 2003, Mar. 2007, Assosiate Professor, Faculty of Science, Nara Women's University
  • Aug. 1996, Jun. 2003, Lecturer, Faculty of Science, Nara Women's University
  • Oct. 1994, Jul. 1996, Research Assistant, Faculty of Sciences, Nara Women's University


  • Apr. 1994, Sep. 1994, The University of Tokyo, Graduate School, Division of Mathematical Sciences, 数理科学
  • Apr. 1992, Mar. 1994, The University of Tokyo, Graduate School, Division of Mathematical Sciences
  • Apr. 1988, Mar. 1992, The University of Tokyo, Faculty of Science, 数学科

Association Memberships

  • 日本数学会
  • 情報処理学会


Published Papers

  • Refereed, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Springer Verlag, Crowdsourcing Mechanism Design, Yuko Sakurai; Masafumi Matsuda; Masato Shinoda; Satoshi Oyama, Crowdsourcing is becoming increasingly popular in various tasks. Although the cost incurred by workers in crowdsourcing is lower than that by experts, the possibility of errors in the former generally exceeds that of the latter. One of the important approaches to quality control of crowdsourcing is based on mechanism design, which has been used to design a game’s rules/protocols so that agents have incentives to truthfully declare their preferences, and designers can select socially advantageous outcomes. Thus far, mechanism design has been conducted by professional economists or computer scientists. However, it is difficult to recruit professional mechanism designers, and developed mechanisms tend to be difficult for people to understand. Crowdsourcing requesters have to determine how to assign tasks to workers and how to reward them. Therefore, a requester can be considered to be an “amateur mechanism designer”. This paper introduces the “wisdom of the crowd” approach to mechanism design, i.e., using crowdsourcing to explore the large design space of incentive mechanisms. We conducted experiments to show that crowd mechanism designers can develop sufficiently diverse candidates for incentive mechanisms and they can choose appropriate mechanisms given a set of candidate mechanisms. We also studied how the designers’ theoretical, economic, and social tendencies, as well as their views on the world, justifiably affect the mechanisms they propose., 2017, 10621, 495, 503, International conference proceedings
  • Refereed, Proceedings of the Third AAAI Conference on Human Computation and Crowdsourcing, HCOMP 2015, November 8-11, 2015, San Diego, California., AAAI Press, Flexible Reward Plans to Elicit Truthful Predictions in Crowdsourcing., Yuko Sakurai; Satoshi Oyama; Masato Shinoda; Makoto Yokoo, 2015, 28, 29
  • Refereed, PRIMA 2015: PRINCIPLES AND PRACTICE OF MULTI-AGENT SYSTEMS, SPRINGER-VERLAG BERLIN, Flexible Reward Plans for Crowdsourced Tasks, Yuko Sakurai; Masato Shinoda; Satoshi Oyama; Makoto Yokoo, We develop flexible reward plans to elicit truthful predictive probability distribution over a set of uncertain events from workers. In general, strictly proper scoring rules for categorical events only reward a worker for an event that actually occurred. However, different incorrect predictions vary in quality, and the principal would like to assign different rewards to them, according to her subjective similarity among events; e.g. a prediction of overcast is closer to sunny than rainy. We propose concrete methods so that the principal can assign rewards for incorrect predictions according to her similarity between events. We focus on two representative examples of strictly proper scoring rules: spherical and quadratic, where a worker's expected utility is represented as the inner product of her truthful predictive probability and her declared probability. In this paper, we generalize the inner product by introducing a reward matrix that defines a reward for each prediction-outcome pair. We first show that if the reward matrix is symmetric and positive definite, both the spherical and quadratic proper scoring rules guarantee the maximization of a worker's expected utility when she truthfully declares her prediction. We next compare our rules with the original spherical/quadratic proper scoring rules in terms of the variance of rewards obtained by workers. Finally, we show our experimental results using Amazon Mechanical Turk., 2015, 9387, 400, 415, International conference proceedings
  • Refereed, 知能と情報(日本知能情報ファジィ学会誌), 人間側から見るコンピュータ将棋の強さ, SHINODA Masato, Nov. 2014, 26, 5, 204-211
  • Refereed, ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, IMPA, Uniform spanning trees on Sierpinski graphs, Masato Shinoda; Elmar Teufl; Stephan Wagner, We study spanning trees on Sierpinski graphs (i.e., finite approximations to the Sierpinski gasket) that are chosen uniformly at random. We construct a joint probability space for uniform spanning trees on every finite Sierpinski graph and show that this construction gives rise to a multi-type Galton-Watson tree. We derive a number of structural results, for instance on the degree distribution. The connection between uniform spanning trees and loop-erased random walk is then exploited to prove convergence of the latter to a continuous stochastic process. Some geometric properties of this limit process, such as the Hausdorff dimension, are investigated as well. The method is also applicable to other self-similar graphs with a sufficient degree of symmetry., 2014, 11, 2, 737, 780, Scientific journal
  • Refereed, Proceedings of the Twelfth International Conference on Autonomous Agents and Multiagent Systems (AAMAS2013), Quality-Control Mechanism utilizing Worker's Confidence for Crowdsourced Tasks, SHINODA Masato; Yuko Sakurai; Tenda Okimoto; Masaaki Oka; Haruhiko Hyodo; Makoto Yokoo, 2013, 1347-1348
  • Refereed, Proceedings of Conference on Human Computation & Croudsourcing, Ability Grouping of Crowd Workers via Reward Discrimination, SHINODA Masato, 2013
  • Refereed, 合同エージェントワークショップ&シンポジウム2012, クラウドソーシングにおける品質コントロールの一考察, SHINODA Masato, Oct. 2012
  • Refereed, IPSJ Journal, Optimal strategy for 3*N AB games, SHINODA Masato, Jun. 2012, 53, 6, 1-6
  • Refereed, IPSJ Symposium Series, Winning strategy of the memory game, SHINODA Masato, Nov. 2008, 2008, 11, 181-188, 188
  • Refereed, PROBABILITY THEORY AND RELATED FIELDS, SPRINGER-VERLAG, Non-existence of phase transition of oriented percolation on Sierpinski carpet lattices, M Shinoda, A percolation problem on Sierpinski carpet lattices is considered. It is obtained that the critical probability of oriented percolation is equal to 1. In contrast it was already shown that the critical probability p(c) of percolation is strictly less than 1 in Kumagai [9]. This result shows a difference between fractal-like lattice and Z(d) lattice., Mar. 2003, 125, 3, 447, 456, Scientific journal
  • Refereed, JOURNAL OF APPLIED PROBABILITY, APPLIED PROBABILITY TRUST, Existence of phase transition of percolation on Sierpnski carpet lattices, M Shinoda, We study Bernoulli bond percolation on Sierpinski carpet lattices, which is a class of graphs corresponding to generalized Sierpinski carpets. In this paper we give a sufficient condition for the existence of a phase transition on the lattices. The proof is suitable for graphs which have self-similarity. We also discuss the relation between the existence of a phase transition and the isoperimetric dimension., Mar. 2002, 39, 1, 1, 10, Scientific journal
  • Refereed, Transactions of the Materials Research Society of Japan, Lower estimate for the critical line of contact processes, Masato SHINODA, 2001, 26, 1, 389, 392
  • Refereed, Osaka Journal of Mathematics, Percolation on the pre-Sierpinski gasket, Masato SHINODA, 1996, 33, 2, 533, 554, Scientific journal
  • Refereed, ゲームプログラミングワークショップ2022論文集, Number-Guessing Game introducing a Reward and a Failure Cost, Riku Yoshioka; Yuko Sakurai; Satoshi Oyama; Masato Shinoda, Nov. 2022, 2022, 25, 28
  • Refereed, ゲームプログラミングワークショップ2022論文集, Determining the Winner of Split-and-delete Nim, Tomoaki Abuku; Ko Sakai; Masato Shinoda; Koki Suetsugu, Nov. 2022, 2022, 17, 24
  • Refereed, PRIMA 2022: Principles and Practice of Multi-Agent Systems, Springer International Publishing, Sample Complexity of Learning Multi-value Opinions in Social Networks, Masato Shinoda; Yuko Sakurai; Satoshi Oyama, 2023, 192, 207, In book


  • Not Refereed, 教育システム研究(奈良女子大学教育システム研究開発センター), 奈良女子大学教育システム研究開発センター, 求積法の変遷を探る学習-高等学校数学科授業の多角的観点からの検討-, SHINODA Masato, Oct. 2017, 別冊, 0, 95-100, 100
  • Not Refereed, IPSJ SIG Technical Report, A Cat-and-Mouse game on the set of integers, SHINODA Masato; Etsuko Sugiyama, Jul. 2017
  • Not Refereed, 第27回人工知能学会全国大会, 人工知能学会, クラウドソーシングにおける必要ワーカ数の動的決定方法の提案, SHINODA Masato, 2013, 27, 1, 3
  • Not Refereed, 第27回人工知能学会全国大会, 人工知能学会, クラウドソーシングでのタスク品質改善のための価格設定の検討, SHINODA Masato, 2013, 27, 1, 3
  • Not Refereed, COE Lecture Note Series (Institute of Mathematics for Industry, Kyushu University), Existence of phase transition of percolation on Sierpinski carpet lattices, SHINODA Masato, Mar. 2012, 39, 12-21
  • Not Refereed, IPSJ SIG Technical Report, Optimal strategy of the memory game with special cards, SHINODA Masato; SAKAMOTO Kanami, Jun. 2010
  • Not Refereed, 研究報告ゲーム情報学(GI), Generalizations of Delete Nim Game and determining the winner, Masato SHINODA, Mar. 2022, 2022-GI-47, 5, 1, 8, Technical report
  • 情報処理学会研究報告, 拡張削除ニム, 安福智明; 坂井公; 篠田正人; 末續鴻輝, Jul. 2022, 2022-GI-48, 14, 1, 5
  • 第36回人工知能学会全国大会, ソーシャルネットワーク上での意見傾向推定のために必要なサンプル数の評価, 篠田 正人; 櫻井 祐子; 小山 聡, Jun. 2022

Books etc

  • 人間に勝つコンピュータ将棋の作り方, 技術評論社, SHINODA Masato, 分担, Sep. 2012, Not Refereed, 9784774153261
  • 確率論ハンドブック, 丸善出版, SHINODA Masato, 分担, Jul. 2012, 439-442, Not Refereed, 9784621065174
  • 確率論・統計学入門, 共立出版, SHINODA Masato, 筆頭著者, Mar. 2008, Not Refereed
  • Percolation on fractal lattices ; Asymptotic behavior of the correlation length, Advances in Nonlinear Partial Differential Equations and Stochastics, World Scientific, SHINODA Masato, 1998, 331-351頁, Not Refereed
  • Mathematical Models, STRAIGHT, Masato SHINODA, Apr. 2022


  • 篠田 正人, 第4回日本組合せゲーム理論研究集会, 数当てゲームの最適戦略, Oral presentation, Aug. 2020
  • Masato SHINODA, Hanoi University of Science, Existence of phase transition of percolation on fractal lattices, Oral presentation, Oct. 2019
  • SHINODA Masato, 研究集会「確率解析の諸相」, Pre-Sierpinski gasket上のpercolation再訪, Jan. 2018, False
  • SHINODA Masato; Etsuko Sugiyama; Masato Shinoda, IPSJ-SIG, A Cat-and Mouse game on the set of integers, Jul. 2017, 倉敷市芸文館, False
  • SHINODA Masato, 奈良女子大学人間文化研究科2015年度数学と物理学と情報科学の研究交流シンポジウム, 強いコンピュータ将棋を作るための数学, Dec. 2015, 奈良女子大学, False
  • SHINODA Masato, 新潟確率論ワークショップ, 数当てゲームの最適戦略, Dec. 2013, 新潟大学南キャンパス「ときめいと」, False
  • SHINODA Masato; Masato SHINODA, 12th workshop on Stochastic Analysis on Large Scale Interacting Systems, Random spanning trees on Sierpinski gasket graphs, Nov. 2013, Tokyo University, True
  • SHINODA Masato, 日本数学会2013年度秋季総合分科会応用数学分科会, 強いコンピュータ将棋の作り方, Sep. 2013, 愛媛大学, False
  • SHINODA Masato, 情報処理学会第74回全国大会, コンピュータ将棋の不思議, Mar. 2012, 名古屋工業大学
  • SHINODA Masato, 新潟確率論ワークショップ, Winning strategy of the memory game, Jan. 2012, 新潟大学, False
  • SHINODA Masato; Masato SHINODA, Multiscale Mathematics: Hierarchy of Collective Phenomena and Interrelations between Hierarchical Structures, Existence of phase transition of percolation on fractal lattices, Dec. 2011, Institute of Mathematics for Industry, Kyushu University
  • SHINODA Masato, フラクタルの数学的諸相, pre-Sierpinski gasketでのminimal spanning treeとpercolation, Feb. 2011, False
  • SHINODA Masato, 確率論とその周辺, Random spanning trees on the Sierpinski gasket, Dec. 2010, 京都大学数理解析研究所, False
  • SHINODA Masato; Masato SHINODA, 34th Conference on Stochastic Processes and Their Applications, Random spanning trees on the Sierpinski gasket, Sep. 2010, Senri Life Science Center Building, False
  • SHINODA Masato, 日本数学会, Uniform spanning trees and loop-erased random walks on the pre-Sierpinski gasket, Sep. 2009, False
  • Masato SHINODA, 情報処理学会第47回ゲーム情報学研究発表会, Generalizations of Delete Nim Game and determining the winner, Oral presentation, 18 Mar. 2022, 18 Mar. 2022, 19 Mar. 2022, rm:research_project_id

Research Projects

  • 基盤研究(C), 01 Apr. 2021, 31 Mar. 2025, 21K12191, 数理ゲームを題材とする確率的最適化の研究および機械学習の有効性判定への活用, 篠田 正人; 嶽村 智子, 日本学術振興会, 科学研究費助成事業 基盤研究(C), 奈良女子大学, 3380000, 2600000, 780000, rm:misc;rm:presentations
  • Grant-in-Aid for Scientific Research (B), 01 Apr. 2018, 31 Mar. 2023, 18H03299, Mechanism Design for Self-Organized Crowdsourcing, 櫻井 祐子; 横尾 真; 篠田 正人; 松田 昌史, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B), National Institute of Advanced Industrial Science and Technology, 14950000, 11500000, 3450000, 本研研究課題の目的は,インターネット上において,多数の人々が自律的に協力することで個人では実行不可能な大規模かつ複雑な作業を効率的に行うためのメカニズム設計技術を確立することである.クラウドソーシングは不特定多数の人々に作業を委託する仕組みであるが,品質制御やセキュリティなど技術的課題が未だ多く,個人もしくは少人数でのチーム作業に留まっている.そこで,本研究では,匿名環境下での大規模な組織化の基盤技術として,マルチエージェントシステムのメカニズム設計技術を基に,参加者らが自律的に協力し良い作業品質を導く,自己組織化クラウドソーシングという新たな基盤を構築する.本年度は,安定な組織形成のためのチーム編成技術に関して重点的に研究を行った.特に,ワーカのチーム編成において,ワーカの関係が簡潔に記述されている場合のチーム編成問題,チームの能力が他のチーム編成に影響される場合のチーム編成問題,新たなワーカの参入がチーム編成の安定性に与える影響の分析,ワーカが突然不参加となる場合を考慮したチーム編成に対する安定性の新たな頑健性の提案を行った.これらの研究に関して,マルチエージェントシステムの国際論文誌JAAMAS,制約充足関連の国際論文誌Constraintsに論文掲載,人工知能の難関国際会議AAAI2019に採択などの成果を得ることができた.
  • Grant-in-Aid for Scientific Research (A), 01 Apr. 2012, 31 Mar. 2016, 24244010, Stochastic geometry and dynamics of infinite particle systems interacting with two-dimensional Coulomb potential, Osada Hirofumi; KOTANI Shinichi; KATORI Makoto; SHINPDA Masato; OTOBE Yoshiki, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (A), Kyushu University, 28470000, 21900000, 6570000, We establish a general theory for solving infinite-dimensional stochastic differential equations (ISDE) with symmetry typically appearing in statistical mechanics. In particular, we prove the pathwise uniqueness and the existence of the strong solution under a very general framework. This method is novel, and regards the tail sigma field of the configuration space as a boundary of the ISDE. Furthermore, if the tail sigma field is trivial, then a strong solution exists. If the set of probability-one events is unique, then the pathwise uniqueness of solution holds. The method is effective for the ISDE with logarithmic interaction potentials, which appear in random matrix theory., url
  • Grant-in-Aid for Young Scientists (B), 2009, 2011, 21740075, New classification of fractals by probabilistic models, SHINODA Masato, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B), Nara Women's University, 2470000, 1900000, 570000, We constructed some percolation models and random minimal spanning tree models on fractal-like graphs and studied some properties of these probabilistic models. Especially we showed that there is a difference of critical values between minimal spanning trees and uniform spanning trees., url
  • Grant-in-Aid for Scientific Research (B), 2009, 2011, 21340031, Infinite-dimensional stochastic dynamical systems motivated by random matrices and statistical physics, OSADA Hirofumi; FUNAKI Tadahisa; TANEMURA Hideki; SHIRAI Tomoyuki; KATORI Makoto; OTOBE Yoshiki; SHINODA Masato; YANO Yuko; YANO Kouji, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B), Kyushu University, 16640000, 12800000, 3840000, We have established a general construction theorem and an SDE representation theorem for interacting Brownian motions with 2D Coulomb potentials. We have applied them to the representative random point fields arising from Random Matrix Theory such as Ginibre, Dyson, Bessel random point fields, and have detected and solve the infinite-dimensional stochastic differential equations describing the associated stochastic dynamics. We prove the Palm measures of Ginibre random point field have very strange property that is very different from usual Gibbs measures with Ruelle' s class interaction potentials. We have constructed the time evolutional model of 2D Young diagram and have proved its scaling limit., url
  • Grant-in-Aid for Scientific Research (C), 2007, 2009, 19540129, Research about effects of boundary states on conditional distributions, TOMISAKI Matsuyo; SHINODA Masato; IIZUKA Masaru, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Nara Women's University, 4420000, 3400000, 1020000, The method of harmonic transform is a useful one to analyze some properties of Green kernels and diffusion processes. It should be noted that these Green kernels and diffusion processes are minimal. However minimal stochastic processes are not always treated in applied mathematics such as population genetics. In our research, conditional distributions of non minimal generalized diffusion processes and the effect of asymptotic behavior of sample paths near the boundaries on conditional distributions are investigated., url
  • Grant-in-Aid for Scientific Research (A), 2005, 2008, 17204011, Comprehensive and integrated research of problems motivated by statistical mechanics with stochastic analysis, OSADA Hirofumi; FUNAKI Tadahisa; SHINODA Masato; KUMAGAI Takashi; SHIRAI Tomoyuki; HARA Takashi; FUKAI Yasunari; UTIYAMA Kohei; MATSUMOTO Hiroyuki; TANEMURA Hideki; NAGAHATA Yukio; HIGUCHI Yasunari; MITOMA Itaru; SUGIURA Makoto; KONNNO Norio; KOMORIYA Keishi; OTOBE Yoshiki; YOSHIDA Nobuo; LIANG Song; HANDA Kenji, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (A), Kyushu University, 26910000, 20700000, 6210000, 統計力学は、膨大な自由度-数学的には無限自由度-をもつ系を研究対象とする。この研究では、統計力学に動機づけられた諸問題を、とくに無限次元確率力学系を中心として、確率解析の手法で統一的に研究し、確率場、相互作用粒子系、極限定理に関係する様々な結果を得た。さらに、これらの研究を契機として、Bessel確率積分やフラクタル構造領域の劣ガウス型熱核の評価など、確率解析の理論を発展させた。, url
  • 若手研究(B), 2004, 2006, 16740054, フラクタルグラフでのパーコレーション相転移現象の研究, 篠田 正人, 日本学術振興会, 科学研究費助成事業 若手研究(B), 奈良女子大学, 3100000, 3100000, 平成18年度は、当初計画通りに「フラクタルグラフでの研究の成果と通常のd次元格子モデルとの関係」について研究を進め、その2つのモデルの「橋渡し」と考えられるシェルピンスキガスケットフラクタルと1次元格子の直積グラフにおけるパーコレーション問題を中心に考察をおこなった。このシェルピンスキガスケットとは「有限分離性」を持つ、直観的には「細いボトルネック構造を持つ」グラフであり、統計力学の確率モデルにおいてこの細い部分の影響がどれほど現れるか、というものである。その成果として、単純なフラクタル格子で現れている「ボトルネックの顕著な影響」はここで考察している新たなグラフでは「ある程度緩和」され、フラクタルの性質をある程度保持しつつ平行移動不変格子(非フラクタル)のよい性質も持つことが現在までにわかりつつある。具体的に言えば、最初の問題として「無限連結成分がボトルネックで分離されてバラバラの状態で存在するか、大きな塊の状態で存在するか」があるが、このグラフではパーコレーションの無限連結成分は唯一であり、パラメータに関して2相にしか持たない(中間相がない)、ということがわかった。こうした性質が・他のフラクタル直積グラフでも成り立つかどうか、・他の統計力学モデルでも成り立つかどうか、は(ある程度の予想はできるが)さらに研究を進める必要がある。なお、この研究における論文は現在準備中であり、19年3月の日本数学会統計数学分科会で講演を行い(演題:The number of infinite percolation clusters on some graph products)、19年度に入っていくつかの研究集会でも発表予定である。
  • Grant-in-Aid for Scientific Research (B), 1999, 2002, 11440029, A new approach to the construction of multi-dimensional diffusion processes via Dirichlet forms and iso perimetric inequalities, OSADA Hirofumi; LIANG Song; ISHIGE Kazuhiro; HATTORI Tetsaya; UEMURA Hideaki; SHINODA Masato, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B), Graduate School of Mathematics, Nagoya University, 12900000, 12900000, The purpose of this research is by using a method the head investigator developed to construct diffusion on infinitely ramified fractals such as Sierpinski carpets, configuration spaces and path spaces. These space are outstandingly of interest and hard to construct nice diffusion processes by using usual methods. In case of fractals we construct diffusion processes which are self-similar and reversible with respect to the Hausdroff measures on the fractals. We used here the method of singular time change. As for random fractals we introduce "bubbles" which has a statistical self-similarity. Although we construct diffusion by using our general theory based on Dirichlet form approach, the detailed investigation of them are future's themes. Some new facts about percolation on fractal lattices are discovered. As for infinite particle systems, we construct diffusions whose stationary measures are so-called "determinantal random point fields". This class of probability measures is very interesting because they are related to random matrix theory and special functions such as Airy functions. This class of probability measures Are different from Ruelle's class Gibbs measures and, I suppose, will be studied extensively in future. As for path spaces we construct diffusions whose invariant measures are Gibbs measures on path spaces, which we also constructed in a course of this research.
  • Grant-in-Aid for Scientific Research (B)., 1998, 2000, 10440029, Developments of Analysis on Fractals, HINO Masanod; TAKAHASHI Yoichiro; KIGAMI Jun; KUMAGAI Takashi; SHINODA Masato; MATSUMOTO Hiroyuki, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)., KYOTO UNIVERSITY, 7800000, 7800000, We have established the following results throughout this project. 1. On spectra of self-adjoint operators on fractals We study the short time asymptotics for heat kernels when the self-similarity of the measure and that of the diffusion process are different. In this case, the asymptotics highly depend on the initial points and there is a multi-fractality. We compute the Hausdorff dimension and the paper will appear. Further, we define a family of quasi-distances and show that the Hausdorff dimension can be expressed in a simple way using some special quasi-distance. 2. On stochastic processes on random fractals (1) We construct a diffusion process and study its heat kernel properties on a homogeneous random Sierpinski carpet. (2) We study a short time heat kernel asymptotics for a diffusion process on a random recursive Sierpinski gasket, which does not have spatial symmetries. These results are in our paper that have already appeared. 3. Stochastic analysis on fractals (1) We construct a diffusion process on a (Euclidean) space where countable numbers of disordered media (such as fractals) are embedded. We apply a trace theory of Besov spaces for the proof. The paper has already appeared and we are now working on large deviations for the process. (2) Concerning the "stochastic analysis for stochastic processes with rough paths" studied by T.Lyons, we have not obtained a new result so far. It is one of the future problem to study the detailed properties of the stochastic differential equations established by him.



  • 情報処理学会, ゲーム情報学研究会運営委員, Society
  • Society
  • 日本数学会, 代議員, Society
  • Society
  • 情報処理学会, ゲーム情報学研究運営委員会幹事, Society
  • Society
  • 日本数学会, 評議員, Society
  • Society

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