Matan Harel

collaborators

Showing math.PRShow all

4 papers · 1 filter

math.PR2026

Upper tails for irregular graphs beyond the mean-field regime

Asaf Cohen Antonir, Matan Harel, Frank Mousset +1

Let $G_{n, p}$ be the binomial random graph of density $p$ and let $X_{H}$ be the number of copies of a fixed graph $H$ in $G_{n, p}$ . We prove asymptotically tight bounds on the logar…

math.PR2026

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…

math.PR2024

Upper tails for arithmetic progressions revisited

Matan Harel, Frank Mousset, Wojciech Samotij

Let $X$ be the number of $k$ -term arithmetic progressions contained in the $p$ -biased random subset of the first $N$ positive integers. We give asymptotically sharp estimates on th…

math.PR2024

Macroscopic loops in the loop O(n) model via the XOR trick

Nicholas Crawford, Alexander Glazman, Matan Harel +1

The loop $O (n)$ model is a family of probability measures on collections of non-intersecting loops on the hexagonal lattice, parameterized by a loop-weight $n$ and an edge-weight $…