Zobrazeno 1 - 10
of 89
pro vyhledávání: '"Vincent Tassion"'
Publikováno v:
Probability Theory and Related Fields, 181
Probability Theory and Related Fields
Probability Theory and Related Fields
This paper is studying the critical regime of the planar random-cluster model on $\mathbb Z^2$ with cluster-weight $q\in[1,4)$. More precisely, we prove crossing estimates in quads which are uniform in their boundary conditions and depend only on the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8f9c841f53b70e6904bc56d9843080b0
https://hdl.handle.net/20.500.11850/492823
https://hdl.handle.net/20.500.11850/492823
Publikováno v:
Combinatorics, Probability & Computing, 29 (1)
Given a graph G and a bijection f : E(G) → {1, 2,…,e(G)}, we say that a trail/path in G is f-increasing if the labels of consecutive edges of this trail/path form an increasing sequence. More than 40 years ago Chvátal and Komlós raised the ques
Publikováno v:
Inventiones mathematicae. 216:661-743
The known Pfaffian structure of the boundary spin correlations, and more generally order-disorder correlation functions, is given a new explanation through simple topological considerations within the model's random current representation. This persp
Publikováno v:
Probability Theory and Related Fields. 173:479-490
We prove that for Voronoi percolation on $$\mathbb {R}^d$$ $$(d\ge 2)$$ , there exists $$p_c=p_c(d)\in (0,1)$$ such that For dimension 2, this result offers a new way of showing that $$p_c(2)=1/2$$ . This paper belongs to a series of papers using the
Publikováno v:
Probability Theory and Related Fields. 172:525-581
We study the phase transition of random radii Poisson Boolean percolation: Around each point of a planar Poisson point process, we draw a disc of random radius, independently for each point. The behavior of this process is well understood when the ra
Publikováno v:
Probability Theory and Related Fields. 171:685-708
We consider critical oriented Bernoulli percolation on the square lattice $$\mathbb {Z}^2$$ . We prove a Russo–Seymour–Welsh type result which allows us to derive several new results concerning the critical behavior: The sub-linear polynomial flu
Publikováno v:
Communications in Mathematical Physics. 349:47-107
This article studies the planar Potts model and its random-cluster representation. We show that the phase transition of the nearest-neighbor ferromagnetic q-state Potts model on $${\mathbb{Z}^2}$$ is continuous for $${q \in \{2,3,4\}}$$ , in the sens
Publikováno v:
Communications on Pure and Applied Mathematics. 69:1397-1411
We prove that for Bernoulli percolation on a graph ℤ2×{0,…,k}(k≥0), there is no infinite cluster at criticality, almost surely. The proof extends to finite-range Bernoulli percolation models on ℤ2 that are invariant under π2-rotation and re
Autor:
Vincent Tassion, Hugo Duminil-Copin
Publikováno v:
Sojourns in Probability Theory and Statistical Physics-II ISBN: 9789811502972
In this note, we discuss a generalization of Schramm’s locality conjecture in the case of random-cluster models. We give some partial (modest) answers, and present several related open questions. Our main result is to show that the critical inverse
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::931402d55f599238632b7209d3fbc28e
https://doi.org/10.1007/978-981-15-0298-9_5
https://doi.org/10.1007/978-981-15-0298-9_5
Autor:
Vincent Tassion, Hugo Duminil-Copin
Publikováno v:
Moscow Mathematical Journal
The study of crossing probabilities - i.e. probabilities of existence of paths crossing rectangles - has been at the heart of the theory of two-dimensional percolation since its beginning. They may be used to prove a number of results on the model, i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::098688ed73a4741c789a62c8300238b1