DIRECTED POLYMERS AND THE QUANTUM TODA LATTICE

被引：122
|
作者：
O'Connell, Neil [1 ]
机构：
[1] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England
来源：
ANNALS OF PROBABILITY | 2012年 / 40卷 / 02期
关键词：
Random matrices; Whittaker functions; SIMPLE EXCLUSION PROCESS; PITMANS 2M-X THEOREM; WHITTAKER FUNCTIONS; BROWNIAN MOTIONS; INITIAL CONDITION; RANDOM MATRICES; FREE-ENERGY; REPRESENTATION; EIGENFUNCTIONS; CHAIN;
D O I：
10.1214/10-AOP632
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
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.
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页码：437 / 458
页数：22
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