Advanced Studies in Pure Mathematics 2010; 514 pp; hardcover Volume: 57 ISBN10: 4931469582 ISBN13: 9784931469587 List Price: US$98 Member Price: US$78.40 Order Code: ASPM/57
 The first Seasonal Institute of the Mathematical Society of Japan (MSJSI)"Probabilistic Approach to Geometry" was held at Kyoto University, Japan, on July 28August 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 postpublication. 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  LiYau 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  NonMarkov 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 fixedpoint property of finitely generated groups and an energy of equivariant maps
 N. Juillet  On a method to disprove generalized BrunnMinkowski inequalities
 V. A. Kaimanovich and F. Sobieczky  Stochastic homogenization of horospheric tree products
 N. Kajino  Remarks on nondiagonality conditions for Sierpinski carpets
 T. Kato  Pattern formation from projectively dynamical systems and iterations by families of maps
 T. Kondo  Fixedpoint 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 BishopGromov 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. SaloffCoste  The heat kernel and its estimates
 I. Shigekawa  Nonsymmetric 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
