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Probabilistic Approach to Geometry
Edited by: Motoko Kotani, Tohoku University, Sendai, Japan, and Masanori Hino and Takashi Kumagai, Kyoto University, Japan
A publication of the Mathematical Society of Japan.
 Advanced Studies in Pure Mathematics 2010; 514 pp; hardcover Volume: 57 ISBN-10: 4-931469-58-2 ISBN-13: 978-4-931469-58-7 List Price: US$98 Member Price: US$78.40 Order Code: ASPM/57 The first Seasonal Institute of the Mathematical Society of Japan (MSJ-SI)--"Probabilistic Approach to Geometry"-- was held at Kyoto University, Japan, on July 28-August 8, 2008. The conference aimed to make interactions between geometry and probability theory and to pursue new directions in these 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 at the conference. Readers will benefit from exploring this developing research area. Volumes in this series are freely available electronically 5 years post-publication. Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. Readership Graduate students and research mathematicians interested in geometry and probability theory. Table of Contents S. Aida -- Rough path analysis: An introduction M. Arnaudon and A. Thalmaier -- Li-Yau type gradient estimates and Harnack inequalities by stochastic analysis A. Atsuji -- Estimates on the number of the omitted values by meromorphic functions K. D. Elworthy -- Stochastic flows and geometric analysis on path spaces R. Friedrich -- The global geometry of stochastic Lœwner evolutions R. Fukushima, A. Tanida, and K. Yano -- Non-Markov property of certain eigenvalue processes analogous to Dyson's model K. Hara -- Rough path conditions for smooth paths T. Hattori and A. Kasue -- Functions of finite Dirichlet sums and compactifications of infinite graphs Y. Inahama -- A note on rough differential equations with unbounded coefficients H. Izeki -- A fixed-point property of finitely generated groups and an energy of equivariant maps N. Juillet -- On a method to disprove generalized Brunn-Minkowski inequalities V. A. Kaimanovich and F. Sobieczky -- Stochastic homogenization of horospheric tree products N. Kajino -- Remarks on non-diagonality conditions for Sierpinski carpets T. Kato -- Pattern formation from projectively dynamical systems and iterations by families of maps T. Kondo -- Fixed-point theorems for random groups K. Kuwada -- Couplings of the Brownian motion via discrete approximation under lower Ricci curvature bounds K. Kuwae and T. Shioya -- Infinitesimal Bishop-Gromov condition for Alexandrov spaces H. Matsuzoe -- Statistical manifolds and affine differential geometry S. Ohta -- Optimal transport and Ricci curvature in Finsler geometry Y. Ollivier -- A survey of Ricci curvature for metric spaces and Markov chains V. Pestov -- Concentration of measure and whirly actions of Polish groups L. Saloff-Coste -- The heat kernel and its estimates I. Shigekawa -- Non-symmetric diffusions on a Riemannian manifold A. Takatsu -- On Wasserstein geometry of Gaussian measures S. Watanabe -- A limit theorem in singular regression problem K. Yano -- Two kinds of conditionings for stable Lévy processes T. Yokota -- A gap theorem for ancient solutions to the Ricci flow
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