87 citations · 454 across the 24 of their papers we have counts for
7 papers · 1 filter
Free flags over local rings and powering of high dimensional expanders
Tali Kaufman, Ori Parzanchevski
Powering the adjacency matrix of an expander graph results in a better expander of higher degree. In this paper we seek an analogue operation for high-dimensional expanders. We sho…
Ramanujan Graphs and Digraphs
Ori Parzanchevski
Ramanujan graphs have fascinating properties and history. In this paper we explore a parallel notion of Ramanujan digraphs, collecting relevant results from old and recent papers,…
Random walks on Ramanujan complexes and digraphs
Eyal Lubetzky, Alex Lubotzky, Ori Parzanchevski
The cutoff phenomenon was recently confirmed for random walks on Ramanujan graphs by the first author and Peres. In this work, we obtain analogs in higher dimensions, for random wa…
Spectrum and combinatorics of two-dimensional Ramanujan complexes
Konstantin Golubev, Ori Parzanchevski
Ramanujan graphs have extremal spectral properties, which imply a remarkable combinatorial behavior. In this paper we compute the high dimensional Hodge-Laplace spectrum of Ramanuj…
Mixing in high-dimensional expanders
Ori Parzanchevski
We prove a generalization of the Expander Mixing Lemma for arbitrary (finite) simplicial complexes. The original lemma states that concentration of the Laplace spectrum of a graph…
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…