New classification of fractals by probabilistic models

• Project/Area Number: 21740075
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Nara Women's University
• Principal Investigator: SHINODA Masato 奈良女子大学, 理学部, 准教授 (50271044)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: フラクタル / 確率モデル / 統計力学 / 相転移 / 確率ゲーム / パーコレーション / ランダムウォーク / 全域木 / 臨界確率 / 確率論

Research Abstract

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.

Research Products

• [Journal Article] 3* N AB gameの最適戦略 (2012)
  • Author(s): 篠田正人
  • Journal Title: 情報処理学会論文誌ジャーナル Volume: 53巻6号 Pages: 1-6
  • NAID: 110009423630
  • Peer Reviewed
• [Journal Article] Existence of phase transition of percolation on Sierpinski carpet lattices (2012)
  • Author(s): M. SHINODA
  • Journal Title: COE Lecture Note Series(Institute of Mathematics for Industry, Kyushu University) Volume: Vol.39 Pages: 12-21
• [Journal Article] Existence of phase transition of percolation on Sierpinski car pet lattices (2012)
  • Author(s): M.SHINODA
  • Journal Title: COE Lecture Note Series (Institute of Mathematics for Industry, Kyushu University) Volume: 39 Pages: 12-21
• [Journal Article] 特別なカードを含む神経衰弱ゲームの勝率最大化戦略 (2011)
  • Author(s): 坂元香菜美、篠田正人
  • Journal Title: 情報処理学会研究報告 Volume: GI-24No.7 Pages: 1-7
  • NAID: 110007993286
• [Presentation] Existence of phase transition of percolation on fractal lattices (2011)
  • Author(s): M. SHINODA
  • Organizer: Multiscale Mathematics : Hierarchy of Collective Phenomena and Interrelations between Hierarchical Structures
  • Place of Presentation: Kyushu University
  • Year and Date: 2011-12-09
• [Presentation] Existence of phase transition of percolation on Sierpinski car pet lattices (2011)
  • Author(s): M.SHINODA
  • Organizer: Multiscale Mathematics : Hierarchy of Collective Phenomena and Interrelations between Hierarchical Structures
  • Place of Presentation: Kyushu University(招待講演)
  • Year and Date: 2011-12-09
• [Presentation] Random spanning trees on the Sierpinski gasket (2010)
  • Author(s): M. SHINODA
  • Organizer: 34th Conference on Stochastic Processes and Their Applications
  • Place of Presentation: Senri Life Science Center Building
  • Year and Date: 2010-09-10
• [Presentation] Uniform spanning trees and loop-erased random walks on the pre-Sierpinski gasket (2009)
  • Author(s): 篠田正人
  • Organizer: 日本数学会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-24