145 citations · 1.2k across the 85 of their papers we have counts for
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math.PR2003★ 23 cited
Convergence to equilibrium for finite Markov processes, with application to the Random Energy Model
Pierre MATHIEU, Pierre PICCO
We estimate the distance in total variation between the law of a finite state Markov process at time t, starting from a given initial measure, and its unique invariant measure. We…
math.PR2003★ 3 cited
Isoperimetry and heat kernel decay on percolation clusters
Pierre Mathieu, Elisabeth Remy
We prove that the heat kernel on the infinite Bernoulli percolation cluster in Z^d almost surely decays faster than t^{-d/2}. We also derive estimates on the mixing time for the ra…