Harmonic Functions on Trees and Buildings.

Intro -- 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 groups -- Biased 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 graphs -- The 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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.