123 citations · 404 across the 40 of their papers we have counts for
49 papers
Regular hyperbolic tilings have no eigenfunctions
Asaf Nachmias
We show that the adjacency operator of the -skeleton of any regular tiling of the hyperbolic plane has no nonzero square-integrable eigenfunctions. As a consequence, the same ho…
Topology and dynamics of unimodular random hyperbolic manifolds
Ilya Gekhtman, Nir Lazarovich, Arie Levit +1
We investigate the relationship between the space of ends of a unimodular random hyperbolic manifold and the dynamics of its geodesic flow. We show that having two ends of infinite…
A Tight Bound on Localization of Electrical Flows
Ori Gurel-Gurevich, Asaf Nachmias, Sushant Sachdeva
We prove that for any unweighted graph on n vertices the L1 norm of a unit electric current between the endpoints of a random edge is at most 2 log n. Furthermore, we show that on…
Determinants of Laplacians on converging hyperbolic surfaces
Renan Gross, Guy Lachman, Asaf Nachmias
Let be a sequence of compact hyperbolic surfaces of increasing volume which locally converges to a random rooted surface. We show that if the normalized sum of the reciprocal…
Critical percolation on the discrete torus in high dimensions
Arthur Blanc-Renaudie, Asaf Nachmias
We consider percolation on the discrete torus at , the critical value for percolation on the corresponding infinite lattice , and…
Local limits of determinantal processes
Asaf Nachmias, Yuval Peled
Let be the row space of a signed adjacency matrix of a -free bipartite bi-regular graph in which one part has degree and the other part has degree …