123 citations · 404 across the 40 of their papers we have counts for
5 papers · 2 filters
Unlacing the lace expansion: a survey to hypercube percolation
Remco van der Hofstad, Asaf Nachmias
The purpose of this note is twofold. First, we survey the study of the percolation phase transition on the Hamming hypercube {0,1}^m obtained in the series of papers [9,10,11,24].…
Rate of Convergence for Cardy's Formula
Dana Mendelson, Asaf Nachmias, Samuel S. Watson
We show that crossing probabilities in 2D critical site percolation on the triangular lattice in a piecewise analytic Jordan domain converge with power law rate in the mesh size to…
Non-amenable Cayley graphs of high girth have p_c < p_u and mean-field exponents
Asaf Nachmias, Yuval Peres
In this note we show that percolation on non-amenable Cayley graphs of high girth has a phase of non-uniqueness, i.e., p_c < p_u. Furthermore, we show that percolation and self-avo…
Recurrence of planar graph limits
Ori Gurel-Gurevich, Asaf Nachmias
We prove that any distributional limit of finite planar graphs in which the degree of the root has an exponential tail is almost surely recurrent. As a corollary, we obtain that th…
Hypercube percolation
Remco van der Hofstad, Asaf Nachmias
We study bond percolation on the Hamming hypercube {0,1}^m around the critical probability p_c. It is known that if p=p_c(1+O(2^{-m/3})), then with high probability the largest con…