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.
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© 1986 Springer-Verlag
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Sullivan, W.G. (1986). L2 convergence of certain random walks on Zd and related diffusions. In: Tautu, P. (eds) Stochastic Spatial Processes. Lecture Notes in Mathematics, vol 1212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076253
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DOI: https://doi.org/10.1007/BFb0076253
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16803-4
Online ISBN: 978-3-540-47053-3
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