Neil O'Connell
Published 2009-10-01, updated 2012-03-28Version 7
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.
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)
Journal: Annals of Probability 2012, Vol. 40, No. 2, 437-458
Geometric RSK and the Toda lattice
Sharp $L^q$-Convergence Rate in $p$-Wasserstein Distance for Empirical Measures of Diffusion Processes
Diffusion semigroup on manifolds with time-dependent metrics
![QR code for arXiv:0910.0069 [math.PR]](http://oss.arxitics.com/images/favicon.svg)