• Corpus ID: 250088921

KPZ limit theorems

@inproceedings{Baik2022KPZLT,
  title={KPZ limit theorems},
  author={Jinho Baik},
  year={2022}
}
  • J. Baik
  • Published 28 June 2022
  • Mathematics
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… 

References

SHOWING 1-10 OF 98 REFERENCES

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

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

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

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

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

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.

  • GwaSpohn
  • Physics
    Physical 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

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

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

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

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
...