Improved Bounds for Mixing Rates of Marked Chains and Multicommodity Flow

In recent years, Markov chain simulation has emerged as a powerful algorithmic paradigm. Its chief application is to the random sampling of combinatorial structures from a specified probability distribution. Such a sampling procedure lies at the heart of efficient probabilistic algorithms for a wide variety of problems, such as approximating the size of combinatorially defined sets, estimating the expectation of certain operators in statistical physics, and combinatorial optimisation by stochastic search.

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