相关论文: KPZ and Airy limits of Hall-Littlewood random plan…

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 consider the asymmetric simple exclusion process (ASEP) on the positive integers with an open boundary condition. We show that, when starting devoid of particles and for a certain boundary condition, the height function at the origin…

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 the KPZ universality class in a periodic…

We study a family of distributions that arise in critical unitary random matrix ensembles. They are expressed as Fredholm determinants and describe the limiting distribution of the largest eigenvalue when the dimension of the random…

We establish a general version of the strong KPZ universality conjecture near the axis for random walks in a random environment (RWRE) on $\mathbb{Z}^2$. For an i.i.d. elliptic random environment, we consider the quenched large deviations…

We identify the key features of Kardar-Parisi-Zhang universality class in the fluctuations of the wave density logarithm, in a two-dimensional Anderson localized wave packet. In our numerical analysis, the fluctuations are found to exhibit…

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.

We express the gap probabilities of the tacnode process as the ratio of two Fredholm determinants; the denominator is the standard Tracy-Widom distribution, while the numerator is the Fredholm determinant of a very explicit kernel…

We prove that the joint distribution of the values of the height function for the stochastic six vertex model in a quadrant along a down-right path coincides with that for the lengths of the first columns of partitions distributed according…

The theory of diffusion seeks to describe the motion of particles in a chaotic environment. Classical theory models individual particles as independent random walkers, effectively forgetting that particles evolve together in the same…

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 special self-similar solutions of the KP…

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…

We show that singular numbers (also known as invariant factors or Smith normal forms) of products and corners of random matrices over $\mathbb{Q}_p$ are governed by the Hall-Littlewood polynomials, in a structurally identical manner to the…

We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate by duplication of columns. Despite the null global curvature, we show that all…

We use the optimal fluctuation method to evaluate the short-time probability distribution $\mathcal{P}\left(H,L,t\right)$ of height at a single point, $H=h\left(x=0,t\right)$, of the evolving Kardar-Parisi-Zhang (KPZ) interface…

We consider the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height $h(x,t)$ on the positive half line with boundary condition $\partial_x h(x,t)|_{x=0}=A$. It is equivalent to a continuum directed polymer…

The Macdonald symmetric functions are used to define measures on the set of all partitions of all integers. Probabilistic algorithms are given for growing partitions according to these measures. The case of Hall-Littlewood polynomials is…

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 the q-TASEP that is a q-deformation of the totally asymmetric simple exclusion process (TASEP) on Z for q in [0,1) where the jump rates depend on the gap to the next particle. For step initial condition, we prove that the…

Exciton-polaritons under driven-dissipative conditions exhibit a condensation transition which belongs to a different universality class than equilibrium Bose-Einstein condensates. By numerically solving the generalized Gross-Pitaevskii…