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 KardarParisiZhang regime with step initial condition, we determine the conditional probability (asymptotically as t → ∞) that a particle is the beginning of an Lblock, 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:

Journal of Mathematical Physics
 Pub Date:
 September 2018
 DOI:
 10.1063/1.5021353
 arXiv:
 arXiv:1711.08094
 Bibcode:
 2018JMP....59i1401T
 Keywords:

 Mathematical Physics;
 Mathematics  Probability;
 60K35
 EPrint:
 19 pages. Version 2 has a new title and an added section on asymptotics for gaps