The interchange process with reversals on the complete graph

Jakob Björnberg, Michał Kotowski, Benjamin T Lees, Piotr Miłos ́

Research output: Contribution to journalArticle (Academic Journal)peer-review


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(1/2) 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.
Original languageEnglish
Number of pages43
JournalElectronic Journal of Probability
Publication statusPublished - 2018


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