2017/11/30 by Craig A. Tracy, Harold Widom
Decision Sciences · Mathematics · Physics and Astronomy · #Asymmetric simple exclusion process #Block (permutation group theory) #Conditional probability #Duality (order theory) #Particle (ecology) #Probability and Risk Models #Probability distribution #Random Matrices and Applications #Simple (philosophy) #Stochastic process #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR #msc:60K35
paper · pdf · doi:10.1063/1.5021353
published as Journal of Mathematical Physics 59, 091401 (2018) · 19 pages. Version 2 has a new title and an added section on asymptotics for gaps
arxiv created 2017/12/10 · openalex created_date 2018/01/12 · openalex publication_date 2018/06/21 · arxiv updated 2018/07/04 · openalex updated_date 2026/08/06
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.