On the spectral gap of the Kac walk and other binary collision processes

Details On the spectral gap of the Kac walk and other binary collision processes On the spectral gap of the Kac walk and other binary collision processes

2008-07-22

arxiv.org/abs/0807.3415v1

ALEA Latin American Journal Of Probability And Mathematical Statistics 4, 205-222 (2008)

Mathematics

Probability

19 pages; to be published in ALEA, Latin American Journal Of Probability And Mathematical Statistics

Scientific paper

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.

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