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2019 The interchange process with reversals on the complete graph
Jakob E. Björnberg, Michał Kotowski, Benjamin Lees, Piotr Miłoś
Electron. J. Probab. 24: 1-43 (2019). DOI: 10.1214/19-EJP366

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.

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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

Information

Received: 25 April 2019; Accepted: 18 September 2019; Published: 2019
First available in Project Euclid: 2 October 2019

zbMATH: 07142902
MathSciNet: MR4017126
Digital Object Identifier: 10.1214/19-EJP366

Subjects:
Primary: 60J27, 60K35

JOURNAL ARTICLE
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Vol.24 • 2019
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