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($\tfrac{1} {2}$) 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.
Citation
Jakob E. Björnberg. Michał Kotowski. Benjamin Lees. Piotr Miłoś. "The interchange process with reversals on the complete graph." Electron. J. Probab. 24 1 - 43, 2019. https://doi.org/10.1214/19-EJP366
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