Abstract
We prove an isoperimetric inequality for wreath products of Markov chains with variable fibers. We use isoperimetric inequalities for wreath products to estimate the return probability of random walks on infinite groups and graphs, drift of random loops, the expected value E(exp(−tR n )), where R n is the number of distinct sites, visited up to the moment n, and, more generally, (where L z,n is the number of visits of z up to the moment n and F(x, y) is some non-negative function).
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Erschler, A. Isoperimetry for wreath products of Markov chains and multiplicity of selfintersections of random walks. Probab. Theory Relat. Fields 136, 560–586 (2006). https://doi.org/10.1007/s00440-005-0495-7
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DOI: https://doi.org/10.1007/s00440-005-0495-7