The interchange process with reversals on the complete graph

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

interchange process

XXZ model

Poisson-Dirichlet distribution

heisenberg models

system

Mathematics

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