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- Shahrzad Haddadan, Peter Winkler
- STACS
- 2017

Markov chains defined on the set of permutations of 1, 2, . . . , n have been studied widely by mathematicians and theoretical computer scientists [15, 4, 1]. We consider chains in which a position i < n is chosen uniformly at random, and then σ(i) and σ(i+1) are swapped with probability depending on σ(i) and σ(i+1). Our objective is to identify some… (More)

In 1995, Jerrum proved a rapid mixing property on a certain Markov chain to solve the problem of sampling uniformly at random from the set of all proper k-colorings on a graph with maximum degree ∆. Jerrum’s proof was for the colorings for which k > 2∆. In 1999, Vigoda improved this bound to k > 11 6 ∆. There has been no improvement for this problem after… (More)

The jaggedness of an order ideal I in a poset P is the number of maximal elements in I plus the number of minimal elements of P not in I . A probability distribution on the set of order ideals of P is toggle-symmetric if for every p ∈ P , the probability that p is maximal in I equals the probability that p is minimal not in I . In this paper, we prove a… (More)

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