Blocks and gaps in the asymmetric simple exclusion process: Asymptotics
Abstract
In earlier work, the authors obtained formulas for the probability in the asymmetric simple exclusion process that at time t, a particle is at site x and is the beginning of a block of L consecutive particles. Here we consider asymptotics. Specifically, for the Kardar-Parisi-Zhang regime with step initial condition, we determine the conditional probability (asymptotically as t → ∞) that a particle is the beginning of an L-block, given that it is at site x at time t. Using duality between occupied and unoccupied sites, we obtain the analogous result for a gap of G unoccupied sites between the particle at x and the next one.
- Publication:
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Journal of Mathematical Physics
- Pub Date:
- September 2018
- DOI:
- 10.1063/1.5021353
- arXiv:
- arXiv:1711.08094
- Bibcode:
- 2018JMP....59i1401T
- Keywords:
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- Mathematical Physics;
- Mathematics - Probability;
- 60K35
- E-Print:
- 19 pages. Version 2 has a new title and an added section on asymptotics for gaps