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Percolation of the excursion sets of planar symmetric shot noise fields

Autor: Raphael Lachieze-Rey, Stephen Muirhead

Compared to the previous version the results about the phase transition have changed slightly: we now establish a phase transition with respect to the level under a log-concavity assumption on the mark distribution, whereas without this assumption we

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ef782780901fe9c51549cd7db0f55fef
http://arxiv.org/abs/1910.14504

The phase transitions of the random-cluster and Potts models on slabs with $q \geq 1$ are sharp

Autor: Aran Raoufiï, Ioan Manolescu

Publikováno v: Electron. J. Probab.

We prove sharpness of the phase transition for the random-cluster model with $q \geq 1$ on graphs of the form $\mathcal{S} := \mathcal{G} \times S$, where $\mathcal{G}$ is a planar lattice with mild symmetry assumptions, and $S$ a finite graph. That

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fb56bd15ee66d846e21faa8a1921417f
http://doc.rero.ch/record/323412/files/man_ptr.pdf

The sharp phase transition for level set percolation of smooth planar Gaussian fields

Autor: Stephen Muirhead, Hugo Vanneuville

Publikováno v: Ann. Inst. H. Poincaré Probab. Statist. 56, no. 2 (2020), 1358-1390

We prove that the connectivity of the level sets of a wide class of smooth centred planar Gaussian fields exhibits a phase transition at the zero level that is analogous to the phase transition in Bernoulli percolation. In addition to symmetry, posit

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::12bcd611194b441318857f30563e5ca5
https://hal.archives-ouvertes.fr/hal-01828330

Sharp phase transitions and critical behaviour in 2D divide and colour models

Autor: Ronald Meester, Federico Camia, András Bálint

Publikováno v: Stochastic Processes and Their Applications, 119, 937-965. Elsevier
Meester, R W J, Balint, A & Camia, F 2009, ' Sharp phase transitions and critical behaviour in 2D divide and colour models ', Stochastic Processes and Their Applications, vol. 119, pp. 937-965 . https://doi.org/10.1016/j.spa.2008.04.003

Consider subcritical Bernoulli bond percolation with fixed parameter p
Comment: 39 pages, 4 figures

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c1a62e24479cb4e6fab2ea0738c8c56a
https://hdl.handle.net/1871/27237