Harmonic functions on trees and buildings : Workshop on Harmonic Functions on Graphs, October 30-November 3, 1995, City University of New York / Adam Korányi, editor ; with minicourses by D. Cartwright [and three others]
Published
Providence, Rhode Island : American Mathematical Society, [1997]
Contents -- Preface -- Part I. Minicourses. -- Local fields and trees -- Martin boundaries and random walks -- A brief introduction to buildings -- Local fields and buildings -- Part II. Abstracts of Lectures. -- Heat kernel for regular trees -- Tensor product of spherical representations of the group of automorphisms of a homogeneous tree -- The horocyclic Radon transform on trees -- Eigenfunctions of the Laplacian on a homogeneous tree -- Exotic convergence in theorems of Fatou type -- A spectral gap property for transfer operators
Harmonic functions on discrete subgroups of semi-simple Lie groupsBiased random walks and harmonic functions on the Lamplighter group -- Characterization of the eigenfunctions of the Laplace operators for an affine building of rank 2 -- Free product of representations -- The Jacobian of a finite graph -- Flows and harmonic functions on graphs -- Applications of diffusion processes on trees to mathematical finance -- Characterizing harmonic functions by mean value properties on trees and symmetric spaces -- Factors from buildings
Harnack and Liouville properties on graphsThe spectrum of a directed Cayley graph of a free group -- Factorization of the Green's kernel for non-nearest neighbor random walks -- Harmonic functions for group-invariant random walks
