KP governs random growth off a 1-dimensional substrate

@article{Quastel2022KPGR,
  title={KP governs random growth off a 1-dimensional substrate},
  author={Jeremy Quastel and Daniel Remenik},
  journal={Forum of Mathematics, Pi},
  year={2022},
  volume={10}
}
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… 
Limiting one-point distribution of periodic TASEP
The relaxation time limit of the one-point distribution of the spatially periodic totally asymmetric simple exclusion process is expected to be the universal one point distribution for the models in
Integration by Parts and the KPZ Two-Point Function
In this article we consider the KPZ fixed point starting from a two-sided Brownian motion with an arbitrary diffusion coefficient. We apply the integration by parts formula from Malliavin calculus to
Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy--Widom GOE distribution
We study the distribution of the supremum of the Airy process with $m$ wanderers minus a parabola, or equivalently the limit of the rescaled maximal height of a system of $N$ non-intersecting
From Painlevé to Zakharov–Shabat and beyond: Fredholm determinants and integro-differential hierarchies
As Fredholm determinants are more and more frequent in the context of stochastic integrability, we unveil the existence of a common framework in many integrable systems where they appear. This
Riemann surfaces for KPZ with periodic boundaries
The Riemann surface for polylogarithms of half-integer index, which has the topology of an infinite dimensional hypercube, is studied in relation to one-dimensional KPZ universality in finite volume.
KPZ limit theorems
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
The logarithmic anti-derivative of the Baik-Rains distribution satisfies the KP equation
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
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
Exact Solution of the Macroscopic Fluctuation Theory for the Symmetric Exclusion Process
We present the first exact solution for the time-dependent equations of the macroscopic fluctuation theory (MFT) for the symmetric simple exclusion process by combining a generalization of the
...
...

References

SHOWING 1-10 OF 61 REFERENCES
On the evolution of packets of water waves
We consider the evolution of packets of water waves that travel predominantly in one direction, but in which the wave amplitudes are modulated slowly in both horizontal directions. Two separate
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
Level-spacing distributions and the Airy kernel
On orthogonal and symplectic matrix ensembles
The focus of this paper is on the probability,Eβ(O;J), that a setJ consisting of a finite union of intervals contains no eigenvalues for the finiteN Gaussian Orthogonal (β=1) and Gaussian Symplectic
A SYSTEM OF DIFFERENTIAL EQUATIONS FOR THE AIRY PROCESS
The Airy process is characterized by its $m$-dimensional distribution functions. For $m=1$ it is known that this distribution function is expressible in terms of a solution to Painleve II. We show
Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
AbstractWe compute the limiting distributions of the largest eigenvalue of a complex Gaussian samplecovariance matrix when both the number of samples and the number of variables in each samplebecome
TASEP and generalizations: method for exact solution
The explicit biorthogonalization method, developed in [arXiv:1701.00018] for continuous time TASEP, is generalized to a broad class of determinantal measures which describe the evolution of several
Limiting one-point distribution of periodic TASEP
The relaxation time limit of the one-point distribution of the spatially periodic totally asymmetric simple exclusion process is expected to be the universal one point distribution for the models in
One-sided reflected Brownian motions and the KPZ fixed point
Abstract We consider the system of one-sided reflected Brownian motions that is in variational duality with Brownian last passage percolation. We show that it has integrable transition probabilities,
...
...