Improved Analysis of Higher Order Random Walks and Applications
STOC '20: 52nd Annual ACM SIGACT Symposium on Theory of Computing Chicago IL USA June, 2020(2020)
摘要
The motivation of this work is to extend the techniques of higher order random walks on simplicial complexes to analyze mixing times of Markov chains for combinatorial problems. Our main result is a sharp upper bound on the second eigenvalue of the down-up walk on a pure simplicial complex, in terms of the second eigenvalues of its links. We show some applications of this result in analyzing mixing times of Markov chains, including sampling independent sets of a graph and sampling common independent sets of two partition matroids.
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关键词
spectral gap, Markov chains, random sampling, high dimensional expansion
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