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The interchange process with reversals on the complete graph

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arxiv 1812.03301 v2 pith:6Y2NP5V7 submitted 2018-12-08 math.PR

Jakob E. Björnberg , Micha{l} Kotowski , Benjamin Lees , Piotr Mi{l}oś This is my paper · ORCID
classification math.PR
keywords interchangeprocesscompleteconvergencegraphreversalsaboveappearance
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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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  1. Critical Parameters for Loop and Bernoulli Percolation

    math.PR 2019-08 conditional novelty 7.0 of 10

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

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