Whittaker functions and related stochastic processes

Abstract

We review some recent results on connections between Brownian motion, Whittaker functions, random matrices and representation theory.

v2,v3: minor corrections. v4: revised version, to appear in proceedings of Fall 2010 MSRI semester `Random matrices, interacting particle systems and integrable systems'

References in corpus (9)

• Log-Gamma polymer free energy fluctuations via a Fredholm determinant identity
• Geometric RSK correspondence, Whittaker functions and symmetrized random polymers
• Littelmann paths and brownian paths
• Bounds for scaling exponents for a 1+1 dimensional directed polymer in a Brownian environment
• A multi-layer extension of the stochastic heat equation
• KPZ Scaling Theory and the Semi-discrete Directed Polymer Model
• O'Connell's process as a vicious Brownian motion
• Survival probability of mutually killing Brownian motions and the O'Connell process
• Random ballistic growth and diffusion in symmetric spaces

Cited by in corpus (7)

• Geometric RSK correspondence, Whittaker functions and symmetrized random polymers
• A q-weighted version of the Robinson-Schensted algorithm
• Noncolliding Brownian Motion with Drift and Time-Dependent Stieltjes-Wigert Determinantal Point Process
• Survival probability of mutually killing Brownian motions and the O'Connell process
• The Ghost-Box-Ball System: A Unified Perspective on Soliton Cellular Automata, the RSK Algorithm and Phase Shifts
• A path model for Whittaker vectors
• Determinantal Martingales and Interacting Particle Systems