For every energy-exchange rate exponent gamma in [0,1], the spectral gap of the stochastic exchange model has a lower bound that depends only on gamma and not on the number of particles N.
Caputo: On the spectral gap of the Kac walk and other binary collision processes , ALEA Lat
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Spectral Gap for the Stochastic Exchange Model
For every energy-exchange rate exponent gamma in [0,1], the spectral gap of the stochastic exchange model has a lower bound that depends only on gamma and not on the number of particles N.