L^2 Convergence of Certain Random Walks on Z^d and related Diffusions

Sullivan, W. G. (1984) L^2 Convergence of Certain Random Walks on Z^d and related Diffusions. (Preprint)

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Abstract

One technique for studying the approach to equilibrium of a continuous time Markov process is to consider the restriction to the L^2 space of an invariant distribution. When the process is reversible with respect to this distribution, the generator is a selfadjoint operator. We study the L^2 spectrum of the generator for certain random walks on Z^d, where the reversible invariant distribution is concentrated near the origin and decays rapidly with distance to the origin. For the related diffusions on R^d we find that the generators are unitarily equivalent to Schrödinger operators.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 10 Jul 2018 14:59
Last Modified: 24 Jul 2018 13:34
URI: http://dair.dias.ie/id/eprint/931

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