Probabilistic Approach to Geometry

The first Seasonal Institute of the Mathematical Society of Japan (MSJ-SI) “Probabilistic Approach to Geometry” was held at Kyoto University, Japan, on 28th July 2008 – 8th August, 2008. The conference aimed to make interactions between Geometry and Probability Theory and seek for new directions of those research areas. This volume contains the proceedings, selected research articles based on the talks, including survey articles on random groups, rough paths, and heat kernels by the survey lecturers in the conference. The readers will benefit of exploring in this developing research area.

Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

• Rough Path Analysis: An Introduction (S Aida)
• Li–Yau Type Gradient Estimates and Harnack Inequalities by Stochastic Analysis (M Arnaudon & A Thalmaier)
• Estimates on the Number of the Omitted Values by Eromorphic Functions (A Atsuji)
• Stochastic Flows and Geometric Analysis on Path Spaces (K D Elworthy)
• The Global Geometry of Stochastic Lœwner Evolutions (R Friedrich)
• Non-Markov Property of Certain Eigenvalue Processes Analogous to Dyson's Model (R Fukushima et al.)
• Rough Path Conditions for Smooth Paths (K Hara)
• Functions of Finite Dirichlet Sums and Compactifications of Infinite Graphs (T Hattori & A Kasue)
• A Note on Rough Differential Equations with Unbounded Coefficients (Y Inahama)
• A Fixed-Point Property of Finitely Generated Groups and an Energy of Equivariant Maps (H Izeki)
• On a Method to Disprove Generalized Brunn–Minkowski Inequalities (N Juillet)
• Stochastic Homogenization of Horospheric Tree Products (V A Kaimanovich & F Sobieczky)
• Remarks on Non-Diagonality Conditions for Sierpinski Carpets (N Kajino)
• Pattern Formation from Projectively Dynamical Systems and Iterations by Families of Maps (T Kato)
• Fixed-Point Theorems for Random Groups (T Kondo)
• Couplings of the Brownian Motion via Discrete Approximation Under Lower Ricci Curvature Bounds (K Kuwada)
• Infinitesimal Bishop–Gromov Condition for Alexandrov Spaces (K Kuwae & T Shioya)
• Statistical Manifolds and Affine Differential Geometry (H Matsuzoe)
• Optimal Transport and Ricci Curvature in Finsler Geometry (S-I Ohta)
• A Survey of Ricci Curvature for Metric Spaces and Markov Chains (Y Ollivier)
• Concentration of Measure and Whirly Actions of Polish Groups (V Pestov)
• The Heat Kernel and Its Estimates (L Saloff-Coste)
• Non-Symmetric Diffusions on a Riemannian Manifold (I Shigekawa)
• On Wasserstein Geometry of Gaussian Measures (A Takatsu)
• A Limit Theorem in Singular Regression Problem (S Watanabe)
• Two Kinds of Conditionings for Stable Lévy Processes (K Yano)
• A Gap Theorem for Ancient Solutions to the Ricci Flow (T Yokota)