The Widom-Rowlinson model under spin flip: Immediate loss and sharp recovery of quasilocality

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Date
2016
Volume
2297
Issue
Journal
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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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-a.s. quasilocal regime back to an everywhere Gibbsian regime. At the sharp reentrance time tG > 0 the model is a.s. quasilocal. For the colorsymmetric model there is no reentrance. On the constructive side, for all t > tG, we provide everywhere quasilocal specifications for the time-evolved measures and give precise exponential estimates on the influence of boundary conditions.

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Keywords
Gibbsianness, non-Gibbsianness, point processes, Widom-Rowlinson model, spin-flip dynamics, quasilocality, non almost-sure quasilocality, Gamma-topology
Citation
Jahnel, B., & Külske, C. (2016). The Widom-Rowlinson model under spin flip: Immediate loss and sharp recovery of quasilocality (Vol. 2297). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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