相关论文: Moments Match between the KPZ Equation and the Air…
Our previous work on the one-dimensional KPZ equation with sharp wedge initial data is extended to the case of the joint height statistics at n spatial points for some common fixed time. Assuming a particular factorization, we compute an…
The parabolic Airy process is the Airy$_2$ process minus a parabola, initially defined by its finite-dimensional distributions, which are given by a Fredholm determinant formula with the extended Airy kernel. This process is also the…
In a recent contribution, Dotsenko establishes a Fredholm determinant formula for the two-point distribution of the KPZ equation in the long time limit and starting from narrow wedge initial conditions. We establish that his expression is…
We derive joint factorial moment identities for point processes with Papangelou intensities. Our proof simplifies previous approaches to related moment identities and includes the setting of Poisson point processes. Applications are given…
In 2002, Johansson conjectured that the maximum of the Airy$_2$ process minus the parabola $x^2$ is almost surely achieved at a unique location. This result was proved a decade later by Corwin and Hammond; Moreno Flores, Quastel and…
The problem to establish not only the asymptotic distribution results for statistical estimators but also the moment convergence of the estimators has been recognized as an important issue in advanced theories of statistics. One of the main…
This paper proves the convergence of the narrow wedge solutions of the KPZ equation to the Airy sheet and the directed landscape in the locally uniform topology. This is the first convergence result to the Airy sheet and the directed…
The height fluctuations of the models in the KPZ class are expected to converge to a universal process. The spatial process at equal time is known to converge to the Airy process or its variations. However, the temporal process, or more…
We consider two versions of discrete time totally asymmetric simple exclusion processes (TASEPs) with geometric and Bernoulli random hopping probabilities. For the process mixed with these and continuous time dynamics, we obtain a single…
We consider all totally asymmetric simple exclusion processes (TASEPs) whose transition probabilities are given in the Sch\"utz-type formulas and which jump with homogeneous rates. We show that the multi-point distribution of particle…
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 (KP) equation. Using this relation we…
We consider the KPZ equation in one space dimension with narrow wedge initial condition, $h(x,t=0)=- |x|/\delta$, $\delta\ll 1$. Based on previous results for the weakly asymmetric simple exclusion process with step initial conditions, we…
The KPZ fixed point is a 2d random field, conjectured to be the universal limiting fluctuation field for the height function of models in the KPZ universality class. Similarly, the periodic KPZ fixed point is a conjectured universal field…
We consider the one-dimensional Kardar-Parisi-Zhang (KPZ) equation with half Brownian motion initial condition, studied previously through the weakly asymmetric simple exclusion process. We employ the replica Bethe ansatz and show that the…
In this paper we consider a probability distribution on plane partitions, which arises as a one-parameter generalization of the q^{volume} measure. This generalization is closely related to the classical multivariate Hall-Littlewood…
We obtain several exact results for universal distributions involving the maximum of the Airy$_2$ process minus a parabola and plus a Brownian motion, with applications to the 1D Kardar-Parisi-Zhang (KPZ) stochastic growth universality…
The logarithm of the diagonal matrix element of a high power of a random matrix converges to the Cole-Hopf solution of the Kardar-Parisi-Zhang equation in the sense of one-point distributions.
The KPZ fixed point is a universal limiting space-time random field for the Kardar-Parisi-Zhang universality class. While the joint law of the KPZ fixed point at a fixed time has been studied extensively, the multipoint distributions of the…
We establish a large deviation principle for the Kardar-Parisi-Zhang (KPZ) equation, providing precise control over the left tail of the height distribution for narrow wedge initial condition. Our analysis exploits an exact connection…
An explicit Fredholm determinant formula is derived for the multipoint distribution of the height function of the totally asymmetric simple exclusion process (TASEP) with arbitrary right-finite initial condition. The method is by solving…