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The interchange process with reversals on the complete graph

The interchange process with reversals on the complete graph

We consider an extension of the interchange process on the complete graph, in which a fraction of the transpositions are replaced by ā€˜reversalsā€™. The model is motivated by statistical physics, where it plays a role in stochastic representations of xxz-models. We prove convergence to PD($\tfrac{1} {2}$) of the rescaled cycle ā€¦