Directed polymers and the quantum Toda lattice
Probability
2012-03-29 v7 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.0910.0069,
title = {Directed polymers and the quantum Toda lattice},
author = {Neil O'Connell},
journal= {arXiv preprint arXiv:0910.0069},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AOP632 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)