# KPZ limit theorems

@inproceedings{Baik2022KPZLT, title={KPZ limit theorems}, author={Jinho Baik}, year={2022} }

One-dimensional interacting particle systems, 1+1 random growth models, and two-dimensional directed polymers deﬁne 2d height ﬁelds. The KPZ universality conjecture posits that an appropriately scaled height function converges to a model-independent universal random ﬁeld for a large class of models. We survey limit theorems for a few models and discuss changes that arise in diﬀerent domains. In particular, we present recent results on periodic domains. We also comment on integrable probability…

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SHOWING 1-10 OF 98 REFERENCES

### Fluctuations of the One-Dimensional Polynuclear Growth Model in Half-Space

- Mathematics
- 2004

We consider the multi-point equal time height fluctuations of the one-dimensional polynuclear growth model in half-space. For special values of the nucleation rate at the origin, the multi-layer…

### Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension

- Mathematics
- 2012

We consider two models for directed polymers in space‐time independent random media (the O'Connell‐Yor semidiscrete directed polymer and the continuum directed random polymer) at positive temperature…

### The heat and the landscape I

- Mathematics
- 2020

Heat flows in 1+1 dimensional stochastic environment converge after scaling to the random geometry described by the directed landscape. In this first part, we show that the O'Connell-Yor polymer and…

### KP governs random growth off a 1-dimensional substrate

- Mathematics, PhysicsForum of Mathematics, Pi
- 2022

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.…

### Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions

- Mathematics
- 2013

We construct a family of stochastic growth models in 2 + 1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1 + 1 dimensional growth models in the…

### Bethe solution for the dynamical-scaling exponent of the noisy Burgers equation.

- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1992

We approximate the noisy Burgers equation by the single-step model, alias the asymmetric simple exclusion process. The generator of the corresponding master equation is identical to the ferromagnetic…

### Shape Fluctuations and Random Matrices

- Mathematics
- 1999

Abstract: We study a certain random growth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations,…

### Stochastic six-vertex model

- Mathematics
- 2016

We study the asymmetric six-vertex model in the quadrant with parameters on the stochastic line. We show that the random height function of the model converges to an explicit deterministic limit…

### Stochastic Higher Spin Vertex Models on the Line

- Mathematics
- 2015

We introduce a four-parameter family of interacting particle systems on the line, which can be diagonalized explicitly via a complete set of Bethe ansatz eigenfunctions, and which enjoy certain…

### The directed landscape

- Mathematics
- 2018

The conjectured limit of last passage percolation is a scale-invariant, independent, stationary increment process with respect to metric composition. We prove this for Brownian last passage…