相关论文: On the local fluctuations of last-passage percolat…
The Airy processes describe spatial fluctuations in wide range of growth models, where each particular Airy process arising in each case depends on the geometry of the initial profile. We show how the coupling method, developed in the…
We prove that the Airy process, A(t), locally fluctuates like a Brownian motion. In the same spirit we also show that in a certain scaling limit, the so called discrete polynuclear growth (PNG) process behaves like a Brownian motion.
We consider the system of one-sided reflected Brownian motions which is in variational duality with Brownian last passage percolation. We show that it has integrable transition probabilities, expressed in terms of Hermite polynomials and…
We consider point to point last passage times to every vertex in a neighbourhood of size $\delta N^{\frac{2}{3}}$, distance $N$ away from the starting point. The increments of these last passage times in this neighbourhood are shown to be…
The model of Brownian Percolation has been introduced as an approximation of discrete last-passage percolation models close to the axis. It allowed to compute some explicit limits and prove fluctuation theorems for these, based on the…
The Airy line ensemble is a positive-integer indexed system of random continuous curves whose finite dimensional distributions are given by the multi-line Airy process. It is a natural object in the KPZ universality class: for example, its…
The interplay between two-dimensional percolation growth models and one-dimensional particle processes has been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of…
The Airy line ensemble is a central object in random matrix theory and last passage percolation defined by a determinantal formula. The goal of this paper is to provide a set of tools which allow for precise probabilistic analysis of the…
We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process A(y). The Airy process is stationary, it has continuous…
We obtain a formula for the $n$-dimensional distributions of the Airy$_1$ process in terms of a Fredholm determinant on $L^2(\rr)$, as opposed to the standard formula which involves extended kernels, on $L^2(\{1,...,n\}\times\rr)$. The…
We investigate extended processes given by last-passage times in directed models defined using exponential variables with decaying mean. In certain cases we find the universal Airy process, but other cases lead to non-universal and trivial…
We consider a last-passage directed percolation model in $Z_+^2$, with i.i.d. weights whose common distribution has a finite $(2+p)$th moment. We study the fluctuations of the passage time from the origin to the point $\big(n,n^{\lfloor a…
* ACTIVATED RANDOM WALK MODEL * This is a conservative particle system on the lattice, with a Markovian continuous-time evolution. Active particles perform random walks without interaction, and they may as well change their state to…
We show that classical integrable models of last passage percolation and the related nonintersecting random walks converge uniformly on compact sets to the Airy line ensemble. Our core approach is to show convergence of nonintersecting…
We study $n$ non-intersecting Brownian motions, corresponding to the eigenvalues of an $n\times n$ Hermitian Brownian motion. At the boundary of their limit shape we find that only three universal processes can arise: the Pearcey process…
In this paper we will prove a shape theorem for the last passage percolation model on a two dimensional $F$-compound Poisson process, called the Hammersley model with random weights. We will also provide diffusive upper bounds for shape…
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 percolation. We construct the Airy sheet and…
Putting dynamics into random matrix models leads to finitely many nonintersecting Brownian motions on the real line for the eigenvalues, as was discovered by Dyson. Applying scaling limits to the random matrix models, combined with Dyson's…
In this paper we consider an equilibrium last-passage percolation model on an environment given by a compound two-dimensional Poisson process. We prove an $\LL^2$-formula relating the initial measure with the last-passage percolation time.…
We study $n$ non-intersecting Brownian motions corresponding to initial configurations which have a vanishing density in the large $n$ limit at an interior point of the support. It is understood that the point of vanishing can propagate up…