The spectral gap of the KMP, harmonic, and immediate exchange models on arbitrary graphs is comparable to, and sometimes exactly equal to, the spectral gap of a natural random walk.
Spectral Gap for the Stochastic Exchange Model
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We prove a spectral gap inequality for the stochastic exchange model studied by Gaspard and Gilbert and by Grigo, Khanin and Sz\'asz in connection with understanding heat conduction in a deterministic billiards model. The bound on the spectral gap that we prove is uniform in the number of particles, as had been conjectured. We adapt techniques that were originally developed to prove spectral gap bounds for the Kac model with hard sphere collisions, which, like the stochastic exchange model, has degenerate jump rates.
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Spectral gap of the KMP and other stochastic exchange models on arbitrary graphs
The spectral gap of the KMP, harmonic, and immediate exchange models on arbitrary graphs is comparable to, and sometimes exactly equal to, the spectral gap of a natural random walk.