Construction of the canonical Brownian motion on moduli space of curves and illustration of its application to stochastic analysis

• Project/Area Number: 21654022
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Osaka University
• Principal Investigator: MORITA Takehiko 大阪大学, 大学院・理学研究科, 教授 (00192782)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥3,270,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥270,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2010: ¥1,000,000 (Direct Cost: ¥1,000,000); Fiscal Year 2009: ¥1,100,000 (Direct Cost: ¥1,100,000)
• Keywords: 確率解析 / ランダム力学系 / タイヒミュラー空間論 / ブラウン運動 / 1次元力学系 / 熱力学形式 / タイヒミュラー空間 / 生成作用素 / ディリクレ形式

Research Abstract

We construct candidates of the canonical Brownian motions on Teichmtiller space via two ways. Although we are not so successful in illustrating an example of application of them, we obtain three auxiliary results. The first is concerned with generic properties of optimization measure for expanding maps, the second is concerned with harmonic measure for a class of mapping tori, and the third is concerned with one-dimensional random dynamical systems.

Research Products

• [Journal Article] Generalization of the continued fraction transformation and the Selberg zeta functions (2012)
  • Author(s): Morita, T.
  • Journal Title: 数理解析研究所講究録 Pages: 1-20
• [Journal Article] Renormalized Rauzy Veech Zorich inductions (2009)
  • Author(s): Morita, T.
  • Journal Title: Comtemp. Math. Volume: 484 Pages: 135-131
  • Peer Reviewed
• [Journal Article] Renormalized Rauzy-Veech-Zorich inductions (2009)
  • Author(s): Takehiko Morita
  • Journal Title: Contemp.Match. 484 Pages: 135-151
  • Peer Reviewed
• [Presentation] Spectral decomposition of one-dimensional random dynamical systems (2011)
  • Author(s): 盛田健彦
  • Organizer: Control and Noise in Dynamical System(Part2)
  • Place of Presentation: 北海道大学大学院理学研究科
  • Year and Date: 2011-08-30
• [Presentation] Spectral decomposition of one-dimensional random dynamical systems (2011)
  • Author(s): T.Morita
  • Organizer: Control and Noise in Dynamical Systems (Part 2)
  • Place of Presentation: 北海道大学大学院理学研究科
  • Year and Date: 2011-08-30
• [Presentation] Measures with maximal total exponents of C^1expanding maps (2010)
  • Author(s): 徳永裕介;盛田健彦
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学大学院多元数理科学研究科
  • Year and Date: 2010-09-22
• [Presentation] Measures with maximum total exponent of C^1 expnading maps (2010)
  • Author(s): 徳永裕介
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-22
• [Presentation] Harmonic measures for aclass of mapping tori (2009)
  • Author(s): 盛田健彦
  • Organizer: 解析学の最近の話題とその周辺から
  • Place of Presentation: 広島大学大学院理学研究科
  • Year and Date: 2009-10-09
• [Presentation] Harmonic measures for a class of mapping tori (2009)
  • Author(s): 盛田健彦
  • Organizer: 解析学の最近の話題とその周辺から
  • Place of Presentation: 広島大学
  • Year and Date: 2009-10-09