Abstract
For the infinite-volume simple symmetric nearest-neighbor exclusion process in one dimension, we investigate the speed of convergence to equilibrium from a particular initial distribution. We use duality to reduce the analysis to that of the two-particle process, which we further reduce to a random walk reflecting rightward at zero, whose generator is self-adjoint on l 2(Z). We obtain the spectral representation of the generator and use asymptotic analysis to show that convergence is slow.
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Keisling, J.D. Convergence Speed for Simple Symmetric Exclusion: An Explicit Calculation. Journal of Statistical Physics 90, 1003–1013 (1998). https://doi.org/10.1023/A:1023297524887
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DOI: https://doi.org/10.1023/A:1023297524887