On the duality between particles and polymers

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.