Amazon.com description: Product Description: This book covers the interplay between the behavior of a class of stochastic processes (random walks) and structure theory. This collection of invited papers by leading researchers presents links with spectral theory and discrete potential theory, besides probabilistic and structure theoretic aspects. Its interdisciplinary approach spans several areas of mathematics including geometric group theory, discrete geometry and harmonic analysis. The work will be of interest to researchers and postgraduate students, both in mathematics and statistical physics.