# Hydrodynamics of the Binary Contact Path Process

## TL;DR

This paper establishes a hydrodynamic limit for the binary contact path process on high-dimensional lattices, showing it converges to a heat equation, with adaptations of existing methods to handle unbounded states.

## Contribution

It extends hydrodynamic limit results to the binary contact path process, adapting techniques for unbounded state spaces.

## Key findings

- Hydrodynamic limit is a heat equation.
- Method adapts to unbounded states.
- Provides a rigorous mathematical framework.

## Abstract

In this paper we are concerned with the binary contact path process introduced in \cite{Gri1983} on the lattice $\mathbb{Z}^d$ with $d\geq 3$. Our main result gives a hydrodynamic limit of the process, which is the solution to a heat equation. The proof of our result follows the strategy introduced in \cite{kipnis+landim99} to give hydrodynamic limit of the SEP model with some details modified since the states of all vertices are not uniformly bounded for the binary contact path process. In the modifications, the theory of the linear system introduced in \cite{Lig1985} is utilized.