2020/11/17 by Joe P. Chen, Milton Jara, Chen, Joe P. +3
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Markov Chains and Monte Carlo Methods #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2011.08718
We prove a general theorem on cutoffs for symmetric simple exclusion processes on graphs with open boundaries, under the natural assumption that the graphs converge geometrically and spectrally to a compact metric measure space with Dirichlet boundary condition. Our theorem is valid on a variety of settings including, but not limited to: the d-dimensional grid for every integer dimension d; and self-similar fractal graphs and products thereof. Our method of proof is to identify a rescaled version of the density fluctuation field---the cutoff martingale---which allows us to prove the mixing time upper bound that matches the lower bound obtained via Wilson's method.