We consider a flip dynamics for directed (1+d)-dimensional lattice paths with length L. The model can be interpreted as a higher dimensional version of the simple exclusion process, the latter corresponding to the case d=1. We prove that the mixing time of the associated Markov chain scales like L^2\log L up to a d-dependent multiplicative constant. The key step in the proof of the upper bound is to show that the system satisfies a logarithmic Sobolev inequality on the diffusive scale L^2 for every fixed d, which we achieve by a suitable induction over the dimension together with an estimate for adjacent transpositions. The lower bound is obtained with a version of Wilson's argument for the one-dimensional case.
Keywords: exclusion process, adjacent transpositions, logarithmic Sobolev inequality, mixing time
Original language | English |
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Publisher | s.n. |
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Number of pages | 22 |
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Publication status | Published - 2015 |
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Name | arXiv |
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Volume | 1504.02354 [math.PR] |
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