Duality for stochastic models of transport

Abstract

We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process which is obtained by placing the system in contact with proper reservoirs, working at different particles densities or different temperatures. We show that all the models are exactly solvable by duality, using a dual process with absorbing boundaries. The solution does also apply to the so-called thermalization limit in which particles or energy is instantaneously redistributed among sites. The results shows that duality is a versatile tool for analyzing stochastic models of transport, while the analysis in the literature has been so far limited to particular instances. Long-range correlations naturally emerge as a result of the interaction of dual particles at the microscopic level and the explicit computations of covariances match, in the scaling limit, the predictions of the macroscopic fluctuation theory.

final revised version, to appear on J. Stat. Phys., 37 pages

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Cited by in corpus (59)

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• Duality in stochastic processes from the viewpoint of basis expansions
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• Markov duality and Bethe ansatz formula for half-line open ASEP
• Hyperuniformity in mass transport processes with center-of-mass conservation: Some exact results
• Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective
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