On the spectral gap of the Kac walk and other binary collision processes
Probability
2010-10-05 v1 Mathematical Physics
math.MP
Abstract
We give a new and elementary computation of the spectral gap of the Kac walk on the N-sphere. The result is obtained as a by-product of a more general observation which allows to reduce the analysis of the spectral gap of an N-component system to that of the same system for N=3. The method applies to a number of random 'binary collision' processes with complete-graph structure, including non-homogeneous examples such as exclusion and colored exclusion processes with site disorder.
Keywords
Cite
@article{arxiv.0807.3415,
title = {On the spectral gap of the Kac walk and other binary collision processes},
author = {Pietro Caputo},
journal= {arXiv preprint arXiv:0807.3415},
year = {2010}
}
Comments
19 pages; to be published in ALEA, Latin American Journal Of Probability And Mathematical Statistics