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Lack of Spectral Gap and Hyperbolicity in Asymptotic Erdös-Renyi Random Graphs
Spectral Gap Hyperbolicity Asymptotic Erdö s-Renyi Random Graphs
2010/12/14
In this work, we prove the absence of a spectral gap for the normalized Laplacian of the Erdos-Renyi random graph G(n; p) when p = d n for d > 1 as n ! 1. We also prove that for any positive the Er...
SPECTRAL GAP ESTIMATE FOR STABLE PROCESSES ON ARBITRARY BOUNDED OPEN SETS
Isotropic stable process spectral gap
2009/9/18
In the paper we prove the lower bound estimate ¸D
2 −¸D
1
c(¸D
1 )−d=®(diamD)−d−® for the spectral gap of the Dirichlet fractional
Laplacia...
On the spectral gap of the Kac walk and other binary collision processes
Spectral gap Conservative dynamics Exclusion processes
2009/6/12
On the spectral gap of the Kac walk and other binary collision processes.
We show that the spectral gap for the interchange process (and the symmetric exclusion process) in a d-dimensional box of side length L is asymptotic to π2/L2. This gives more evidence in favor of Ald...