Directed polymers and the quantum Toda lattice

By Neil O'Connell. 2009

217 citations recorded by the source corpus.

We characterize the law of the partition function of a Brownian directed polymer model in terms of a diffusion process associated with the quantum Toda lattice. The proof is via a multidimensional generalization of a theorem of Matsumoto and Yor concerning exponential functionals of Brownian motion. It is based on a mapping which can be regarded as a geometric variant of the RSK correspondence.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/681bd1288e5cc931a26dd19559677e78004d05b0

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In Discrete Mathematics and Combinatorics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

From duality to determinants for q-TASEP and ASEP (2012, methodology): “That result is not entirely elementary as it relies upon the convergence of q-Whittaker processes to Whittaker processes [8] as well as the relationship of Whittaker processes to the semi-discrete directed polymer [29].”
Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension (2012, methodology): “1, due to O’Connell’s work [50] on a continuum version of tropical RSK correspondence, the partition function Z (t) arises as a marginal of the Whittaker process (or measure).”
Height Fluctuations for the Stationary KPZ Equation (2014, methodology): “We now define a class of Whittaker processes which are composites of those which arose in [37, 65].”
Macdonald processes (2011, methodology): “However, in Part 6 we will demonstrate a new ansatz for computing polymer moments which applies equally well to both models.”