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We study the mixing time of a Markov chain Mnn on permutations that performs nearest neighbor transpositions in the non-uniform setting, a problem arising in the context of self-organizing lists. We are given " positively biased " probabilities {pi,j ≥ 1/2} for all i < j and let pj,i = 1 − pi,j. In each step, the chain Mnn chooses two adjacent elements k,(More)
Sampling permutations from S n is a fundamental problem from probability theory. The nearest neighbor transposition chain M nn is known to converge in time Θ(n 3 log n) in the uniform case [18] and time Θ(n 2) in the constant bias case, in which we put adjacent elements in order with probability p = 1/2 and out of order with probability 1 − p [2]. Here we(More)
The Schelling Segregation Model was proposed by Thomas Schelling in 1971 as a means of explaining possible causes of racial segregation in cities. He considered residents of two types, say red and blue, where each person prefers the majority of his or her neighbors to have the same color. He showed through simulations that even mild preferences of this type(More)
Graded posets frequently arise throughout combinatorics, where it is natural to try to count the number of elements of a fixed rank. These counting problems are often #P-complete, so we consider approximation algorithms for counting and uniform sampling. We show that for certain classes of posets, biased Markov chains that walk along edges of their Hasse(More)
We consider perfect matchings of the square-octagon lattice, also known as " fortresses " [16]. There is a natural local Markov chain on the set of perfect matchings that is known to be ergodic. However, unlike Markov chains for sampling perfect matchings on the square and hexagonal lattices, corresponding to domino and lozenge tilings, respectively, the(More)
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