Simple Random Walks on Tori |
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| Authors: | Sinai Ya. G. |
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| Affiliation: | (1) Department of Mathematics, Princeton University, Princeton, New Jersey, and;(2) Landau Institute of Theoretical Physics, Moscow, Russia |
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| Abstract: | We consider a Markov chain whose phase space is a d-dimensional torus. A point x jumps to x+ with probability p(x) and to x– with probability 1–p(x). For Diophantine and smooth p we prove that this Markov chain has an absolutely continuous invariant measure and the distribution of any point after n steps converges to this measure. |
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| Keywords: | Markov chain homological equation Levy excursion stable law |
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