Formulas for ASEP with Two-Sided Bernoulli Initial Condition

TL;DR

This paper derives exact formulas for key probabilistic quantities in the ASEP with two-sided Bernoulli initial conditions, advancing understanding of particle dynamics and correlations in this stochastic process.

Contribution

It provides new exact formulas for site occupation probabilities, correlation functions, and flux distribution in ASEP with two-sided Bernoulli initial conditions.

Findings

Exact formula for site occupation probability at position x and time t.

Correlation function between initial and later site occupations.

Distribution and generating function for total flux across site 0.

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.