KP控制着一维基底上的随机生长

IF 2.8 1区数学 Q1 MATHEMATICS

Forum of Mathematics Pi Pub Date : 2019-08-27 DOI:10.1017/fmp.2021.9

J. Quastel, Daniel Remenik

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引用次数: 26

摘要

摘要一维随机波动界面边缘分布的对数导数根据Kadomtsev–Petviashvili（KP）方程在大尺度上演化。这是从[MQR17]中获得的Kardar–Parisi–Zhang（KPZ）不动点的Fredholm行列式代数推导而来的，该不动点是TASEP的转移概率的极限，TASEP是KPZ普适性类中的一个特殊可解模型。Tracy–Widom分布表现为KP和Korteweg–de Vries方程的特殊自相似解。此外，值得注意的是，KPZ方程的几种已知精确解也能求解KP方程。

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KP governs random growth off a 1-dimensional substrate

Abstract The logarithmic derivative of the marginal distributions of randomly fluctuating interfaces in one dimension on a large scale evolve according to the Kadomtsev–Petviashvili (KP) equation. This is derived algebraically from a Fredholm determinant obtained in [MQR17] for the Kardar–Parisi–Zhang (KPZ) fixed point as the limit of the transition probabilities of TASEP, a special solvable model in the KPZ universality class. The Tracy–Widom distributions appear as special self-similar solutions of the KP and Korteweg–de Vries equations. In addition, it is noted that several known exact solutions of the KPZ equation also solve the KP equation.

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来源期刊

Forum of Mathematics Pi Mathematics-Statistics and Probability

CiteScore

3.50

自引率

0.00%

发文量

审稿时长

19 weeks

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