A Multi-Layer Extension of the Stochastic Heat Equation

被引：0
作者：
Neil O’Connell
Jon Warren
机构：
[1] University of Warwick,Mathematics Institute
[2] University of Warwick,Department of Statistics
来源：
Communications in Mathematical Physics | 2016年 / 341卷
关键词：
Markov Property; Darboux Transformation; Brownian Bridge; Asymmetric Simple Exclusion Process; Directed Polymer;
D O I：
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学科分类号：
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.
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页码：1 / 33
页数：32
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