• Corpus ID: 224803806

A System of PDEs for the Baik-Rains Distribution

  title={A System of PDEs for the Baik-Rains Distribution},
  author={Xincheng Zhang},
  journal={arXiv: Probability},
It has been discovered that the Kadomtsev-Petviashvili(KP) equation governs the distribution of the fluctuation of many random growth models, in particular, the Tracy-Widom distributions appear as special self-similar solutions of the KP equation. We prove that the anti-derivative of Baik-Rains distribution, which governs the fluctuation of the models in the KPZ universality class starting with stationary initial data, satisfies the KP equation. We start from a determinantal formula of the… 
1 Citations

Integrable fluctuations in the KPZ universality class

A BSTRACT . The KPZ fixed point is a scaling invariant Markov process which arises as the universal scaling limit of a broad class of models of random interface growth in one dimension, the



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.

Large deviations for the KPZ equation from the KP equation

Recently, Quastel and Remenik \cite{QRKP} [arXiv:1908.10353] found a remarkable relation between some solutions of the finite time Kardar-Parisi-Zhang (KPZ) equation and the Kadomtsev-Petviashvili

Height Fluctuations for the Stationary KPZ Equation

We compute the one-point probability distribution for the stationary KPZ equation (i.e. initial data H(0,X)=B(X)$\mathcal {H}(0,X)=B(X)$, for B(X) a two-sided standard Brownian motion) and show that

General determinants and the tau function for the Kadomtsev-Petviashvili hierarchy

The tau function, introduced by the 'Kyoto School' as a central element in the description of soliton equation hierarchies, is identified with the determinant of a family of linear operators solving

Limiting Distributions for a Polynuclear Growth Model with External Sources

The purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources which was considered by Prähofer and Spohn. Depending on the

Functional Analysis I

A vector space over a field K (R or C) is a set X with operations vector addition and scalar multiplication satisfy properties in section 3.1. [1] An inner product space is a vector space X with

We need to showK b,β →K b,b uniformly on compact set