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 |
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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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