Summary
We consider the one-dimensional weakly asymmetric nearest neighbour exclusion process and study its macroscopic behaviour on a longer time scale than that for which the deterministic approximation by the Burgers equation holds. We show that this long-time behaviour is completely determined by the initial particle configuration, and does not depend on the randomness of the evolution. Moreover, we examine in detail a special case for which a travelling wave is observed with stable profile but randomly fluctuating space location.
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Dittrich, P. Travelling waves and long-time behaviour of the weakly asymmetric exclusion process. Probab. Th. Rel. Fields 86, 443–455 (1990). https://doi.org/10.1007/BF01198168
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DOI: https://doi.org/10.1007/BF01198168
Keywords
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Burger Equation
- Initial Particle