Determinantal structures in the O'Connell-Yor directed random polymer model

Abstract

We study the semi-discrete directed random polymer model introduced by O'Connell and Yor. We obtain a representation for the moment generating function of the polymer partition function in terms of a determinantal measure. This measure is an extension of the probability measure of the eigenvalues for the Gaussian Unitary Ensemble (GUE) in random matrix theory. To establish the relation, we introduce another determinantal measure on larger degrees of freedom and consider its few properties, from which the representation above follows immediately.

45 pages, 2 figures

References in corpus (13)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Fluctuation properties of the TASEP with periodic initial configuration
• An exact solution for the KPZ equation with flat initial conditions
• The KPZ equation with flat initial condition and the directed polymer with one free end
• Random-walk in Beta-distributed random environment
• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
• KPZ equation limit of higher-spin exclusion processes
• The strict-weak lattice polymer
• A Pfaffian representation for flat ASEP
• Brownian Motions with One-Sided Collisions: The Stationary Case
• Renormalization Group and Stochastic PDE's
• System of Complex Brownian Motions Associated with the O'Connell Process

Cited by in corpus (11)

• Non-interacting fermions at finite temperature in a $d$-dimensional trap: universal correlations
• The ASEP and determinantal point processes
• Moments Match between the KPZ Equation and the Airy Point Process
• Airy kernel determinant solutions to the KdV equation and integro-differential Painlevé equations
• Tilted elastic lines with columnar and point disorder, non-Hermitian quantum mechanics and spiked random matrices: pinning and localization
• Stochastic higher spin six vertex model and Madconald measures
• Free energy distribution of the stationary O'Connell-Yor directed random polymer model
• Interacting diffusions on positive definite matrices
• Central moments of the free energy of the O'Connell-Yor polymer
• Correlation kernels for sums and products of random matrices
• On the $q$-TASEP with a random initial condition