On the duality between particles and polymers

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.

final version after minor revisions

References in corpus (13)

• Shape Fluctuations and Random Matrices
• Discrete polynuclear growth and determinantal processes
• Fluctuation properties of the TASEP with periodic initial configuration
• Exact Solution of the Master Equation for the Asymmetric Exclusion Process
• Spatial correlations of the 1D KPZ surface on a flat substrate
• Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems
• The Airy_1 process is not the limit of the largest eigenvalue in GOE matrix diffusion
• Determinantal transition kernels for some interacting particles on the line
• Reflected Brownian motions in the KPZ universality class
• A multi-dimensional Markov chain and the Meixner ensemble
• One-sided reflected Brownian motions and the KPZ fixed point
• TASEP and generalizations: Method for exact solution
• TASEP with a general initial condition and a deterministically moving wall