Jahnel, Benedikt; Külske, Christof The Widom – Rowlinson model under spin flip: immediate loss and sharp recovery of quasilocality. (English) Zbl 1390.82039 Ann. Appl. Probab. 27, No. 6, 3845-3892 (2017). Summary: 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. Cited in 8 Documents MSC: 82C21 Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics 60K35 Interacting random processes; statistical mechanics type models; percolation theory Keywords:Gibbsianness; non-Gibbsianness; point processes; Widom – Rowlinson model; spin-flip dynamics; quasilocality; non-almost-sure quasilocality; \(\tau\)-topology × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid References: [1] Bollobás, B. and Riordan, O. (2006).Percolation. Cambridge Univ. Press, New York. · Zbl 1118.60001 [2] Bricmont, J., Kuroda, K. and Lebowitz, J. L. (1984). 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