58 citations · 106 across the 14 of their papers we have counts for
11 papers · 1 filter
Upper tails for irregular graphs beyond the mean-field regime
Asaf Cohen Antonir, Matan Harel, Frank Mousset +1
Let be the binomial random graph of density and let be the number of copies of a fixed graph in . We prove asymptotically tight bounds on the logar…
Planar percolation and the loop O(n) model
Alexander Glazman, Matan Harel, Nathan Zelesko
We show that a large class of site percolation processes on any planar graph contains either zero or infinitely many infinite connected components. The assumptions that we require…
Upper tails for arithmetic progressions revisited
Matan Harel, Frank Mousset, Wojciech Samotij
Let be the number of -term arithmetic progressions contained in the -biased random subset of the first positive integers. We give asymptotically sharp estimates on th…
Depinning in integer-restricted Gaussian Fields and BKT phases of two-component spin models
Michael Aizenman, Matan Harel, Ron Peled +1
For a family of integer-valued height functions defined over the faces of planar graphs, we establish a relation between the probability of connection by level sets and the spin-sp…
Macroscopic loops in the loop O(n) model via the XOR trick
Nicholas Crawford, Alexander Glazman, Matan Harel +1
The loop model is a family of probability measures on collections of non-intersecting loops on the hexagonal lattice, parameterized by a loop-weight and an edge-weight $…
Logarithmic variance for the height function of square-ice
Hugo Duminil-Copin, Matan Harel, Benoit Laslier +2
In this article, we prove that the height function associated with the square-ice model (i.e.~the six-vertex model with on the square lattice), or, equivalently, of the u…
Upper tails via high moments and entropic stability
Matan Harel, Frank Mousset, Wojciech Samotij
Suppose that is a bounded-degree polynomial with nonnegative coefficients on the -biased discrete hypercube. Our main result gives sharp estimates on the logarithmic upper t…
Finitary codings for the random-cluster model and other infinite-range monotone models
Matan Harel, Yinon Spinka
A random field on a quasi-transitive graph is a factor of i.i.d. if it can be written as for some i.i.d. process and equivar…
The Bethe ansatz for the six-vertex and XXZ models: an exposition
Hugo Duminil-Copin, Maxime Gagnebin, Matan Harel +2
In this paper, we review a few known facts on the coordinate Bethe ansatz. We present a detailed construction of the Bethe ansatz vector and energy , which satisfy …
Discontinuity of the phase transition for the planar random-cluster and Potts models with
Hugo Duminil-Copin, Maxime Gagnebin, Matan Harel +2
We prove that the -state Potts model and the random-cluster model with cluster weight undergo a discontinuous phase transition on the square lattice. More precisely, we sh…
Localization in random geometric graphs with too many edges
Sourav Chatterjee, Matan Harel
We consider a random geometric graph , given by connecting two vertices of a Poisson point process of intensity on the unit torus whenever their distance is…