Zobrazeno 1 - 10
of 80
pro vyhledávání: '"Manolescu, Ioan"'
Autor:
Manolescu, Ioan, Santoro, Leonardo V.
We answer the following question: if the occupied (or vacant) set of a planar Poisson Boolean percolation model does contain a crossing of an $n\times n$ square, how wide is this crossing? The answer depends on the whether we consider the critical, s
Externí odkaz:
http://arxiv.org/abs/2211.11661
We provide a new proof of the near-critical scaling relation $\beta=\xi_1\nu$ for Bernoulli percolation on the square lattice already proved by Kesten in 1987. We rely on a novel approach that does not invoke Russo's formula, but rather relates diffe
Externí odkaz:
http://arxiv.org/abs/2111.14414
Autor:
Glazman, Alexander, Manolescu, Ioan
Publikováno v:
Prob. Math. Phys. 4 (2023) 209-256
We prove that all Gibbs measures of the $q$-state Potts model on $\mathbb{Z}^2$ are linear combinations of the extremal measures obtained as thermodynamic limits under free or monochromatic boundary conditions. In particular all Gibbs measures are in
Externí odkaz:
http://arxiv.org/abs/2106.02403
We show that the height function of the six-vertex model, in the parameter range $\mathbf a=\mathbf b=1$ and $\mathbf c\ge1$, is delocalized with logarithmic variance when $\mathbf c\le 2$. This complements the earlier proven localization for $\mathb
Externí odkaz:
http://arxiv.org/abs/2012.13750
Autor:
Duminil-Copin, Hugo, Kozlowski, Karol Kajetan, Krachun, Dmitry, Manolescu, Ioan, Oulamara, Mendes
In this paper, we prove that the large scale properties of a number of two-dimensional lattice models are rotationally invariant. More precisely, we prove that the random-cluster model on the square lattice with cluster-weight $1\le q\le 4$ exhibits
Externí odkaz:
http://arxiv.org/abs/2012.11672
Autor:
Duminil-Copin, Hugo, Kozlowski, Karol Kajetan, Krachun, Dmitry, Manolescu, Ioan, Tikhonovskaia, Tatiana
In this paper, we provide new proofs of the existence and the condensation of Bethe roots for the Bethe Ansatz equation associated with the six-vertex model with periodic boundary conditions and an arbitrary density of up arrows (per line) in the reg
Externí odkaz:
http://arxiv.org/abs/2012.11675
Autor:
Duminil-Copin, Hugo, Manolescu, Ioan
This paper studies the critical and near-critical regimes of the planar random-cluster model on $\mathbb Z^2$ with cluster-weight $q\in[1,4]$ using novel coupling techniques. More precisely, we derive the scaling relations between the critical expone
Externí odkaz:
http://arxiv.org/abs/2011.15090
Publikováno v:
Probability Theory and Related Fields volume 181, 401-449 (2021)
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:
http://arxiv.org/abs/2007.14707
We study randomly growing trees governed by the affine preferential attachment rule. Starting with a seed tree $S$, vertices are attached one by one, each linked by an edge to a random vertex of the current tree, chosen with a probability proportiona
Externí odkaz:
http://arxiv.org/abs/1810.13275
Autor:
Glazman, Alexander, Manolescu, Ioan
We show that the loop $O(n)$ model on the hexagonal lattice exhibits exponential decay of loop sizes whenever $n> 1$ and $x<\tfrac{1}{\sqrt{3}}+\varepsilon(n)$, for some suitable choice of $\varepsilon(n)>0$. It is expected that, for $n \leq 2$, the
Externí odkaz:
http://arxiv.org/abs/1810.11302