# Blocks in ASEP with step-Bernoulli initial condition

## TL;DR

This paper extends the analysis of blocks in ASEP to step-Bernoulli initial conditions, deriving a Fredholm determinant representation and analyzing asymptotics in the KPZ regime.

## Contribution

It introduces a Fredholm determinant formula for blocks in ASEP with step-Bernoulli initial condition and computes their asymptotics in the KPZ regime.

## Key findings

- Fredholm determinant representation for block probabilities
- Asymptotic analysis in the KPZ regime
- Extension of Tracy-Widom results to step-Bernoulli initial conditions

## Abstract

This paper extends work by Tracy and Widom on blocks in the asymmetric simple exclusion process (ASEP) to the case of step-Bernoulli initial condition. We consider the probability that a particle at site $x$ is the beginning of a block of $L$ consecutive particles at time $t$ in ASEP with step-Bernoulli initial condition. A Fredholm determinant representation for this probability is derived, and the asymptotics are computed for the KPZ regime.