The interchange process with reversals on the complete graph
Journal article, 2019

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) of the rescaled cycle sizes, above the critical point 2 for the appearance of macroscopic cycles. This extends a result of Schramm on convergence to PD(1) for the usual interchange process.

Interchange process

Poisson-Dirichlet distribution

XXZ model


Jakob Björnberg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Michał Kotowski

University of Warsaw

Benjamin Lees

Technische Universität Darmstadt

Piotr Miłoś

Polish Academy of Sciences

Electronic Journal of Probability

1083-6489 (ISSN)

Vol. 24 108

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis



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