Random polymers via orthogonal Whittaker and symplectic Schur functions

Understand

This thesis deals with some $(1+1)$-dimensional lattice path models from the KPZ universality class: the directed random polymer with inverse-gamma weights (known as log-gamma polymer) and its zero temperature degeneration, i.e.

• the last passage percolation model, with geometric or exponential waiting times.
• We consider three path geometries: point-to-line, point-to-half-line, and point-to-line with paths restricted to stay in a half-plane.
• Through exact formulas, we establish new connections between integrable probabilistic models and the ubiquitous Whittaker and Schur functions.