DIRECTED POLYMERS AND THE QUANTUM TODA LATTICE

• 成果类型: Article
• 署名作者: O'Connell, Neil
• 署名单位: University of Warwick
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP632
• 发表日期: 2012
• 页码: 437-458
• 关键词: simple exclusion process; pitmans 2m-x theorem; whittaker functions; Brownian motions; initial condition; RANDOM MATRICES; free-energy; REPRESENTATION; eigenfunctions; chain

摘要

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.