87 citations · 193 across the 17 of their papers we have counts for
21 papers
Eigenvalues and spectral gap in sparse random simplicial complexes
Shaked Leibzirer, Ron Rosenthal
We consider the adjacency operator of the Linial-Meshulam model for random dimensional simplicial complexes on vertices, where each cell is added indepen…
The chemical distance in random interlacements in the low-intensity regime
Sarai Hernandez-Torres, Eviatar B. Procaccia, Ron Rosenthal
In with , we consider the time constant associated to the chemical distance in random interlacements at low intensity . We prove an upper boun…
Simplicial spanning trees in random Steiner complexes
Ron Rosenthal, Lior Tenenbaum
A spanning tree in a graph is a sub-graph of with the same vertex set as which is a tree. In 1981, McKay proved an asymptotic result regarding the number of spannin…
On the Spectrum of Dense Random Geometric Graphs
Kartick Adhikari, Robert J. Adler, Omer Bobrowski +1
In this paper we study the spectrum of the random geometric graph , in a regime where the graph is dense and highly connected. In the \erdren random graph it is we…
Eigenvector correlations in the complex Ginibre ensemble
Nicholas Crawford, Ron Rosenthal
The complex Ginibre ensemble is an non-Hermitian random matrix over with i.i.d. complex Gaussian entries normalized to have mean zero and variance . U…
Stabilization of DLA in a wedge
Eviatar B. Procaccia, Ron Rosenthal, Yuan Zhang
We consider Diffusion Limited Aggregation (DLA) in a two-dimensional wedge. We prove that if the angle of the wedge is smaller than , there is some such that almost sure…
Isotropic self-consistent equations for mean-field random matrices
Yukun He, Antti Knowles, Ron Rosenthal
We present a simple and versatile method for deriving (an)isotropic local laws for general random matrices constructed from independent random variables. Our method is applicable t…
On groups and simplicial complexes
Alexander Lubotzky, Zur Luria, Ron Rosenthal
The theory of -regular graphs is closely related to group theory. Every -regular, bipartite graph is a Schreier graph with respect to some group , a set of generators …
Random Steiner systems and bounded degree coboundary expanders of every dimension
Alexander Lubotzky, Zur Luria, Ron Rosenthal
We introduce a new model of random -dimensional simplicial complexes, for , whose -cells have bounded degrees. We show that with high probability, complexes samp…
Eigenvalue confinement and spectral gap for random simplicial complexes
Antti Knowles, Ron Rosenthal
We consider the adjacency operator of the Linial-Meshulam model for random simplicial complexes on vertices, where each -cell is added independently with probability to…
Non-metricity in the continuum limit of randomly-distributed point defects
Raz Kupferman, Cy Maor, Ron Rosenthal
We present a homogenization theorem for isotropically-distributed point defects, by considering a sequence of manifolds with increasingly dense point defects. The loci of the defec…
Simplicial branching random walks and their applications
Ron Rosenthal
We define a new stochastic process on general simplicial complexes which allows to study their spectral and homological properties. Some results for random walks on graphs are show…
Local limit theorem and equivalence of dynamic and static points of view for certain ballistic random walks in i.i.d. environments
Noam Berger, Moran Cohen, Ron Rosenthal
In this work, we discuss certain ballistic random walks in random environments on , and prove the equivalence between the static and dynamic points of view in dimensi…
Quenched invariance principle for simple random walk on clusters in correlated percolation models
Eviatar Procaccia, Ron Rosenthal, Artem Sapozhnikov
We prove quenched invariance principle for simple random walk on the unique infinite percolation cluster for a general class of percolation models on Z^d, d>=2, with long-range cor…
Simplicial complexes: spectrum, homology and random walks
Ori Parzanchevski, Ron Rosenthal
Random walks on a graph reflect many of its topological and spectral properties, such as connectedness, bipartiteness and spectral gap magnitude. In the first part of this paper we…
Isoperimetry in two-dimensional percolation
Marek Biskup, Oren Louidor, Eviatar B. Procaccia +1
We consider the unique infinite connected component of supercritical bond percolation on the square lattice and study the geometric properties of isoperimetric sets, i.e., sets wit…
Isoperimetric Inequalities in Simplicial Complexes
Ori Parzanchevski, Ron Rosenthal, Ran J. Tessler
In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expa…
Concentration estimates for the isoperimetric constant of the super critical percolation cluster
Eviatar B. Procaccia, Ron Rosenthal
We consider the Cheeger constant of the giant component of supercritical bond percolation on . We show that the variance of is bounded by…
Behavior of random walk on discrete point processes
Noam Berger, Ron Rosenthal
We consider a model for random walks on random environments (RWRE) with random subset of Z^d as the vertices, and uniform transition probabilities on 2d points (two "coordinate nea…
The need for speed : Maximizing random walks speed on fixed environments
Eviatar B. Procaccia, Ron Rosenthal
We study nearest neighbor random walks on fixed environments of composed of two point types : and for . We show that for every environment…
Random walk on discrete point processes
Ron Rosenthal
We consider a model for random walks on random environments (RWRE) with random subset of the d-dimensional Euclidean lattice as the vertices, and uniform transition probabilities o…