6 citations · 32 across the 10 of their papers we have counts for
4 papers · 1 filter
Combinatorics via Closed Orbits: Number Theoretic Ramanujan Graphs are not Unique Neighbor Expanders
Amitay Kamber, Tali Kaufman
The question of finding expander graphs with strong vertex expansion properties such as unique neighbor expansion and lossless expansion is central to computer science. A barrier t…
Cutoff on Graphs and the Sarnak-Xue Density of Eigenvalues
Konstantin Golubev, Amitay Kamber
It was recently shown by Lubetzky and Peres (2016) and by Sardari (2018) that Ramanujan graphs, i.e., graphs with the optimal spectrum, exhibit cutoff of the simple random walk in…
Lp expander Complexes
Amitay Kamber
We discuss two combinatorical ways of generalizing the definition of expander graphs and Ramanujan graphs, to quotients of buildings of higher dimension. The two possible definitio…
Expander Graphs
Amitay Kamber
We discuss how graph expansion is related to the behavior of -functions on the covering tree. We show that the non-trivial eigenvalues of the adjacency operator on aa $(q+1)…