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 -- Non-commutative 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 3-orbifold
• 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