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On sampling with Markov chains. (English) Zbl 0861.60079
From the authors’ introduction: We apply new eigenvalue bounds for random walks that we call “convex subgraphs” of homogeneous graphs. A principal feature of these techniques is the ability to obtain eigenvalue estimates in situation in which there is a nonempty boundary obstructing the walk, typically a more difficult situation than the boundaryless case. In particular, we will give the first proof of rapid convergence for the “natural” walk on contingency tables, as well as generalizations to restricted contingency tables, symmetric tables, compositions of an integer, and so-called knapsack solutions.
MSC:
60G50Sums of independent random variables; random walks
62H17Contingency tables (statistics)
47A75Eigenvalue problems (linear operators)
60C05Combinatorial probability