KP governs random growth off a 1-dimensional substrate

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

引用次数: 26

Abstract

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.

查看原文本刊更多论文

KP控制着一维基底上的随机生长

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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

期刊介绍： Forum of Mathematics, Pi is the open access alternative to the leading generalist mathematics journals and are of real interest to a broad cross-section of all mathematicians. Papers published are of the highest quality. Forum of Mathematics, Pi and Forum of Mathematics, Sigma are an exciting new development in journal publishing. Together they offer fully open access publication combined with peer-review standards set by an international editorial board of the highest calibre, and all backed by Cambridge University Press and our commitment to quality. Strong research papers from all parts of pure mathematics and related areas are welcomed. All published papers are free online to readers in perpetuity.