# Multi-species Stochastic Model And Effective Stochastic Generator with Site-Dependent Interactions

## TL;DR

This paper explores conditions under which the effective stochastic generators for multi-species particle systems on a lattice can be local and site-dependent, extending previous results from single-species models.

## Contribution

It demonstrates that for multi-species systems with local, site-independent interactions, the effective generators can be made local and site-dependent under certain microscopic constraints.

## Key findings

- Effective generators can be local and site-dependent for multi-species systems.
- Constraints on microscopic rules determine the locality of the effective generator.
- Application to a two-species A-model illustrates these conditions.

## Abstract

The dynamical rules in auxiliary stochastic process that generates the biased ensemble of rare events are non-local. For the systems with one type of particle, it is shown that there are special cases for which the generators of effective processes can include local interactions. In this paper we investigate this possibility for a systems of classical particles with more than one type of particle moving on a one-dimensional lattice with open boundary conditions. Assuming that the interactions in the original process are local and site-independent and also it is assumed that the particles have hard-core interactions. We will show that under certain constraints on the microscopic reaction rules, the stochastic generator of unconditioned process can be local but site-dependent. As one examples, A-model with two species of particles are presented and be investigated the constraints under which the effective generators are local and site-dependent.

---
Source: https://tomesphere.com/paper/1904.13238