A Multi-Layer Extension of the Stochastic Heat Equation

被引：17
|
作者：
O'Connell, Neil [1 ]
Warren, Jon [2 ]
机构：
[1] Univ Warwick, Inst Math, Coventry CV4 7AL, W Midlands, England
[2] Univ Warwick, Dept Stat, Coventry CV4 7AL, W Midlands, England
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2016年 / 341卷 / 01期
基金：
英国工程与自然科学研究理事会;
关键词：
DIMENSIONAL DIRECTED POLYMER; FREE-ENERGY; REGIME;
D O I：
10.1007/s00220-015-2541-3
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Motivated by recent developments on solvable directed polymer models, we define a 'multi-layer' extension of the stochastic heat equation involving non-intersecting Brownian motions. By developing a connection with Darboux transformations and the two-dimensional Toda equations, we conjecture a Markovian evolution in time for this multi-layer process. As a first step in this direction, we establish an analogue of the Karlin-McGregor formula for the stochastic heat equation and use it to prove a special case of this conjecture.
引用
收藏
页码：1 / 33
页数：33
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