Formulas for ASEP with Two-Sided Bernoulli Initial Condition

Abstract

For the asymmetric simple exclusion process on the integer lattice with two-sided Bernoulli initial condition, we derive exact formulas for the following quantities: (1) the probability that site x is occupied at time t; (2) a correlation function, the probability that site 0 is occupied at time 0 and site x is occupied at time t; (3) the distribution function for the total flux across 0 at time t and its exponential generating function.

18 pages

References in corpus (6)

• Shape Fluctuations and Random Matrices
• Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process
• Integral Formulas for the Asymmetric Simple Exclusion Process
• A Fredholm Determinant Representation in ASEP
• Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
• On ASEP with Step Bernoulli Initial Condition

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• Current Fluctuations of the Stationary ASEP and Six-Vertex Model
• Current moments of 1D ASEP by duality
• Crossover distributions at the edge of the rarefaction fan
• Asymmetric Exclusion Process with Global Hopping
• Crystal Growth Inside an Octant
• Tail estimates for the stationary stochastic six vertex model and ASEP
• Distribution of a tagged particle position in the one-dimensional symmetric simple exclusion process with two-sided Bernoulli initial condition