On mixing of certain random walks, cutoff phenomenon and sharp threshold of random matroid processes |
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Authors: | Igor Pak and Van H Vu |
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Institution: | Department of Mathematics, Yale University, New Haven, CT 06520, USA |
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Abstract: | In this paper we define and analyze convergence of the geometric random walks, which are certain random walks on vector spaces over finite fields. We show that the behavior of such walks is given by certain random matroid processes. In particular, the mixing time is given by the expected stopping time, and the cutoff is equivalent to sharp threshold. We also discuss some random geometric random walks as well as some examples and symmetric cases. |
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Keywords: | Random walks Markov chains Random graphs Stopping time Separation distance Cutoff phenomenon Sharp threshold |
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