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The interchange process with reversals on the complete graph

· 2018 · math.PR · arXiv 1812.03301

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abstract

We consider an extension of the interchange process on the complete graph, in which a fraction of the transpositions are replaced by `reversals'. The model is motivated by statistical physics, where it plays a role in stochastic representations of $XXZ$-models. We prove convergence to PD($\tfrac12$) of the rescaled cycle sizes, above the critical point for the appearance of macroscopic cycles. This extends a result of Schramm on convergence to PD(1) for the usual interchange process.

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math.PR 1

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2019 1

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CONDITIONAL 1

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  • Critical Parameters for Loop and Bernoulli Percolation math.PR · 2019-08-27 · conditional · none · ref 36 · internal anchor

    Infinite loops in random loop models on bounded-degree graphs occur strictly later than infinite clusters in the associated Bernoulli percolation.