相关论文: Exceptional times when the KPZ fixed point violate…

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…

Let $\mathfrak h_t$ be the KPZ fixed point started from any initial condition that guarantees $\mathfrak h_t$ has a maximum at every time $t$ almost surely. For any fixed $t$, almost surely $\max \mathfrak h_t$ is uniquely attained.…

The maximal point of the Airy2 process minus a parabola is believed to describe the scaling limit of the end-point of the directed polymer in a random medium, which was proved to be true for a few specific cases. Recently two different…

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…

We show that the increments of the KPZ fixed point started from arbitrary initial data are \emph{mutually} absolutely continuous with respect to Brownian motion with diffusion parameter $2$ on compacts, extending the one-sided Brownian…

The results of Amir-Corwin-Quastel, Calabrese-Le Doussal-Rosso, Dotsenko, and Sasamoto-Spohn imply that the one-point distribution of the solution of the KPZ equation with the narrow wedge initial condition coincides with that for a…

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…

We consider the periodic totally asymmetric simple exclusion process with a general initial condition that properly approximates a periodic upper-semicontinuous function. We find the large time limit of the rescaled space-time multipoint…

The term 'KPZ' stands for the initials of three physicists, namely Kardar, Parisi and Zhang, which, in 1986 conjectured the existence of universal scaling behaviours for many random growth processes in the plane. A process is said to belong…

We consider existence and uniqueness issues for the initial value problem of parabolic equations $\partial_{t} u = {\rm div} A \nabla u$ on the upper half space, with initial data in $L^p$ spaces. The coefficient matrix $A$ is assumed to be…

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…

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 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…

Many models of one-dimensional local random growth are expected to lie in the Kardar-Parisi-Zhang (KPZ) universality class. For such a model, the interface profile at advanced time may be viewed in scaled coordinates specified via…

The Kardar-Parisi-Zhang (KPZ) fixed point is a Markov process that is conjectured to be at the core of the KPZ universality class. In this article we study two aspects the KPZ fixed point that share the same Brownian limiting behaviour: the…

The Kardar-Parisi-Zhang (KPZ) fixed point is a Markov process, recently introduced by Matetski, Quastel, Remenik (arXiv:1701.00018), that describes the limit fluctuations of the height function associated to the totally asymmetric simple…

We show that under the 1:2:3 scaling, critically probing large space and time, the height function of finite range asymmetric exclusion processes and the KPZ equation converge to the KPZ fixed point, constructed earlier as a limit of the…

There has recently been much activity within the Kardar-Parisi-Zhang universality class spurred by the construction of the canonical limiting object, the parabolic Airy sheet $\mathcal{S}:\mathbb{R}^2\to\mathbb{R}$ [arXiv:1812.00309]. The…

The periodic KPZ fixed point is the conjectural universal limit of the KPZ universality class models on a ring when both the period and time critically tend to infinity. For the case of the periodic narrow wedge initial condition, we…

We first show that the Airy$_1$ process is associated using the association property of the solution to the stochastic heat equation and convergence of the KPZ equation to the KPZ fixed point. Then we apply Newman's inequality to establish…