Electronic Journal of Probability

The interchange process with reversals on the complete graph

Jakob E. Björnberg, Michał Kotowski, Benjamin Lees, and Piotr Miłoś

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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.

Article information

Electron. J. Probab., Volume 24 (2019), paper no. 108, 43 pp.

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

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J27: Continuous-time Markov processes on discrete state spaces

interchange process XXZ model Poisson-Dirichlet distribution

Creative Commons Attribution 4.0 International License.


Björnberg, Jakob E.; Kotowski, Michał; Lees, Benjamin; Miłoś, Piotr. The interchange process with reversals on the complete graph. Electron. J. Probab. 24 (2019), paper no. 108, 43 pp. doi:10.1214/19-EJP366. https://projecteuclid.org/euclid.ejp/1569981823

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