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

Understand

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.