Contemporary Mathematics 2004; 258 pp; softcover Volume: 347 ISBN10: 0821833510 ISBN13: 9780821833513 List Price: US$76 Member Price: US$60.80 Order Code: CONM/347
 This book is a collection of papers from the proceedings of the first symposium of the Japan Association for Mathematical Sciences. Topics covered center around problems of geometric analysis in relation to heat kernels, random walks, and Poisson boundaries on discrete groups, graphs, and other combinatorial objects. The material is suitable for graduate students and research mathematicians interested in heat kernels and random works on groups and graphs. Readership Graduate students and research mathematicians interested in heat kernel and random works on groups and graphs. Table of Contents  N. Lohoué and G. Alexopoulos  On the asymptotic behavior of convolution powers and heat kernels on Lie groups
 Y. Higuchi and T. Shirai  Some spectral and geometric properties for infinite graphs
 S. Ishiwata  Asymptotic behavior of a transition probability for a random walk on a nilpotent covering graph
 M. Izumi  Noncommutative Poisson boundaries
 V. A. Kaimanovich  Boundary amenability of hyperbolic spaces
 T. Kato  Spectral analysis on tree like spaces from gauge theoretic view points
 S. Kojima and S. Mizushima  The Dehn filling space of a certain hyperbolic 3orbifold
 M. Kotani  An asymptotic of the large deviation for random walks on a crystal lattice
 B. M. Hambly and T. Kumagai  Heat kernel estimates and law of the iterated logarithm for symmetric random walks on fractal graphs
 A. Lubotzky and Y. Shalom  Finite representations in the unitary dual and Ramanujan groups
 N. Monod  Stabilization for SL\(_n\) in bounded cohomology
 H. Nagoshi  Spectral theory of certain arithmetic graphs
 A. Nevo  Radial geometric analysis on groups
 H. Urakawa  The heat kernel and the Green kernel of an infinite graph
