# Fermionic construction of tau functions and random processes

## TL;DR

This paper demonstrates how fermionic expectation values can naturally describe various random processes and statistical models involving particles on a lattice, offering new tools for analysis and combinatorial calculations.

## Contribution

It introduces a fermionic framework for tau functions that simplifies the description of lattice particle models and enables advanced combinatorial computations.

## Key findings

- Fermionic tau functions effectively model discrete ASEP and related processes.
- The approach simplifies calculations of particle configurations and path enumerations.
- Analysis of initial step function decay in d-ASEP illustrates the method's utility.

## Abstract

Tau functions expressed as fermionic expectation values are shown to provide a natural and straightforward description of a number of random processes and statistical models involving hard core configurations of identical particles on the integer lattice, like a discrete version simple exclusion processes (ASEP), nonintersecting random walkers, lattice Coulomb gas models and others, as well as providing a powerful tool for combinatorial calculations involving paths between pairs of partitions. We study the decay of the initial step function within the discrete ASEP (d-ASEP) model as an example.