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December 2017 The Widom–Rowlinson model under spin flip: Immediate loss and sharp recovery of quasilocality
Benedikt Jahnel, Christof Külske
Ann. Appl. Probab. 27(6): 3845-3892 (December 2017). DOI: 10.1214/17-AAP1298

Abstract

We consider the continuum Widom–Rowlinson model under independent spin-flip dynamics and investigate whether and when the time-evolved point process has an (almost) quasilocal specification (Gibbs-property of the time-evolved measure). Our study provides a first analysis of a Gibbs–non-Gibbs transition for point particles in Euclidean space. We find a picture of loss and recovery, in which even more regularity is lost faster than it is for time-evolved spin models on lattices.

We show immediate loss of quasilocality in the percolation regime, with full measure of discontinuity points for any specification. For the color-asymmetric percolating model, there is a transition from this non-almost-sure quasilocal regime back to an everywhere Gibbsian regime. At the sharp reentrance time $t_{G}>0$, the model is a.s. quasilocal. For the color-symmetric model, there is no reentrance. On the constructive side, for all $t>t_{G}$, we provide everywhere quasilocal specifications for the time-evolved measures and give precise exponential estimates on the influence of boundary condition.

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Benedikt Jahnel. Christof Külske. "The Widom–Rowlinson model under spin flip: Immediate loss and sharp recovery of quasilocality." Ann. Appl. Probab. 27 (6) 3845 - 3892, December 2017. https://doi.org/10.1214/17-AAP1298

Information

Received: 1 September 2016; Revised: 1 March 2017; Published: December 2017
First available in Project Euclid: 15 December 2017

zbMATH: 06848280
MathSciNet: MR3737939
Digital Object Identifier: 10.1214/17-AAP1298

Subjects:
Primary: 82C21
Secondary: 60K35

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.27 • No. 6 • December 2017
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