A Multi-Layer Extension of the Stochastic Heat Equation
A Multi-Layer Extension of the Stochastic Heat Equation
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DOI：
10.1007/s00220-015-2541-3
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发表时间：
2011-04
影响因子：
2.4
通讯作者：
N. O’Connell;J. Warren
中科院分区：
文献类型：
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作者：
N. O’Connell;J. Warren
基于可解定向聚合物模型的最新发展，我们定义了一个涉及非相交布朗运动的随机热方程的“多层”扩展。通过发展与达布变换和二维户田方程的连接，我们推测这个多层过程的时间马尔可夫演化。作为这个方向的第一步，我们建立了一个模拟的Karlin-McGregor公式的随机热方程，并用它来证明这个猜想的一个特殊情况。
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.