Convergence Speed for Simple Symmetric Exclusion: An Explicit Calculation

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 l²(Z). We obtain the spectral representation of the generator and use asymptotic analysis to show that convergence is slow.