Isoperimetric inequalities for Random Walks
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Geometric Random Walks: A Survey∗
The developing theory of geometric random walks is outlined here. Three aspects — general methods for estimating convergence (the “mixing” rate), isoperimetric inequalities in Rn and their intimate connection to random walks, and algorithms for fundamental problems (volume computation and convex optimization) that are based on sampling by random walks — are discussed.
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In this paper necessary and sufficient conditions are presented for heat kernel upper bounds for random walks on weighted graphs. Several equivalent conditions are given in the form of isoperimetric inequalities.
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In this paper necessary and sufficient conditions are presented for heat kernel upper bounds for random walks on weighted graphs. Several equivalent conditions are given in the form of isoperimetric inequalities.
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Contents 1. Introduction 2 2. Basic definitions and preliminaries 3 A. Adaptedness to the graph structure 4 B. Reversible Markov chains 4 C. Random walks on groups 5 D. Group-invariant random walks on graphs 6 E. Harmonic and superharmonic functions 6 3. Spectral radius, amenability and law of large numbers 6 A. Spectral radius, isoperimetric inequalities and growth 6 B. Law of large numbers 9 ...
متن کاملMathav Murugan 1 Gaussian Estimates for Random Walks
My research interests lie at the interface of probability and analysis. The broad goal of my research is to understand how the long-term behavior of Markov chains depends on the large-scale geometry of the underlying state space. In particular, I am interested in heat kernel estimates for discrete time Markov chains on state spaces having a geometric structure, for instance a weighted graph, Ri...
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