87 citations · 193 across the 17 of their papers we have counts for
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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…