On the duality between particles and polymers

TL;DR

This paper investigates the duality between particle systems and polymer models, establishing formulas that connect last passage percolation and tasep, and deriving determinantal formulas for specific boundary conditions.

Contribution

It introduces a duality framework linking tasep and last passage percolation models, providing new determinantal formulas for boundary-specific scenarios.

Findings

Derived determinantal formulas for last passage percolation with deterministic boundary

Established duality relations translating observables between models

Connected tasep particle systems with polymer models through duality

Abstract

We explore the connection between tasep-like interacting particle systems and last passage percolation type polymer models, focusing on three models: Geometric, Exponential and Brownian last passage percolation and their associated tasep particle systems. We explain how formulas for certain natural observables in last passage percolation translate to formulas for tasep, by going through a notion of "duality". In turn, we obtain determinantal formulas for last passage percolation with a deterministic boundary and for tasep with a deterministic first particle trajectory.