The Motion of a Tagged Particle in the Simple Symmetric Exclusion System on $Z$
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In this paper, a simple exclusion interaction is considered where each particle independently attempts to execute a simple symmetric random walk, but any jump which would carry a particle to an already occupied site is suppressed.Abstract:
Consider a system of particles moving on the integers with a simple exclusion interaction: each particle independently attempts to execute a simple symmetric random walk, but any jump which would carry a particle to an already occupied site is suppressed. For the system running in equilibrium, we analyze the motion of a tagged particle. This solves a problem posed in Spitzer's 1970 paper "Interaction of Markov Processes." The analogous question for systems which are not one-dimensional, nearest-neighbor, and either symmetric or one-sided remains open. A key tool is Harris's theorem on positive correlations in attractive Markov processes. Results are also obtained for the rightmost particle in the exclusion system with initial configuration $Z^-$, and for comparison systems based on the order statistics of independent motions on the line.read more
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Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions
TL;DR: In this paper, a functional central limit theorem for additive functionals of stationary reversible ergodic Markov chains was proved under virtually no assumptions other than the necessary ones, and they used these results to study the asymptotic behavior of a tagged particle in an infinite particle system performing simple excluded random walk.
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An invariance principle for reversible Markov processes. Applications to random motions in random environments
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Eigenvalue Bounds on Convergence to Stationarity for Nonreversible Markov Chains, with an Application to the Exclusion Process
TL;DR: In this paper, the mixing rate of a simple exclusion process corresponding to clockwise walk on the discrete circle was shown to rapidly mix when $d$ grows with p. The dense case of mixing with p = p/2 was considered in a Poisson blockers problem in statistical mechanics.