On ASEP with step Bernoulli initial condition. (English) Zbl 1188.82043
The paper extends previous work by the authors on asymmetric exclusion processes to the case of the step Bernoulli initial condition. The crucial technical ingredient is a new combinatorial formula, that allows to set a representation of the probability distribution for a fixed particle in terms of a Fredholm determinant. Among the asymptotic results for this probability distribution, the Kardar-Parisi-Zhang universality is shown to arise in one specific regime.
Reviewer: Piotr Garbaczewski (Opole)
MSC:
| 82C20 | Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics |
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
| 82C23 | Exactly solvable dynamic models in time-dependent statistical mechanics |
Keywords:
asymmetric exclusion process; Kardar-Parisi-Zhang (KPZ) universality; Bethe ansatz; Fredholm determinant; Bernoulli initial conditionReferences:
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