Makiko Sasada (University of Tokyo)
  Mixing rates of stochastic energy exchange models with degenerate rate
  functions.
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Abstract: In recent years, stochastic energy exchange systems of locally
confined particles in interaction have been studied intensively, as
accessible models for the rigorous study of the derivation of Fourier's law
from microscopic dynamics of mechanical origin. As a generalization of them,
Grigo et al. introduced a class of pure jump Markov processes of energies
and studied the spectral gap of them under the assumption that the rate
function of the energy exchange is uniformly positive. In this talk, I will
consider the case where the rate function does not have a uniform lower
bound, and give a lower bound estimate of the spectral gap. The hydrodynamic
behavior of these systems will be also discussed.