相关论文: Duality between coalescence times and exit points …

Using the fact that the Airy process describes the limiting fluctuations of the Hammersley last-passage percolation model, we prove that it behaves locally like a Brownian motion. Our method is quite straightforward, and it is based on a…

Coalescence of semi-infinite geodesics remains a central question in planar first passage percolation. In this paper we study finer properties of the coalescence structure of finite and semi-infinite geodesics for exactly solvable models of…

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 consider two particles performing continuous-time nearest neighbor random walk on $\mathbb Z$ and interacting with each other when they are at neighboring positions. Typical examples are two particles in the partial exclusion process or…

We study the last passage time in geometric last passage percolation (LPP). As the system size increases, we derive precise large deviation probabilities -- up to and including the constant terms -- for both the lower and upper tails. A key…

In this paper, we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are generated by stationary weakly and strongly dependent Gaussian sequences. It is shown that the…

We study the statistics of last-passage time for linear diffusions. First we present an elementary derivation of the Laplace transform of the probability density of the last-passage time, thus recovering known results from the mathematical…

We present some aspects of the so-called additive coalescence, with a focus on its connections with random trees, Brownian excursion, certain bridges with exchangeable increments, L\'evy processes, and sticky particle systems.

The aim of this paper is to study the law of the last passage time of a linear diffusion to a curved boundary. We start by giving a general expression for the density of such a random variable under some regularity assumptions. Following…

The aim of this article is to study the forest composed by point-to-line geodesics in the last-passage percolation model with exponential weights. We will show that the location of the root can be described in terms of the maxima of a…

While coalescence is ultimately the most drastic destabilization process in foams, its underlying processes are still unclear. To better understand them, we track individual coalescence events in two-dimensional foams at controlled…

In this note we investigate the last passage percolation model in the presence of macroscopic inhomogeneity. We analyze how this affects the scaling limit of the passage time, leading to a variational problem that provides an ODE for the…

We present a duality relation between two systems of coalescing random walks and an analogous duality relation between two systems of coalescing Brownian motions. Our results extends previous work in the literature and we apply it to the…

We present new probabilistic and combinatorial identities relating three random processes: the oriented swap process on $n$ particles, the corner growth process, and the last passage percolation model. We prove one of the probabilistic…

Following the recent investigations of Baik and Suidan in \cite{baik2005gcl} and Bodineau and Martin in \cite{bodineau2005upl}, we prove large deviation properties for a last-passage percolation model in $\mathbb{Z}^{2}_{+}$ whose paths are…

The extended Airy kernel describes the space-time correlation functions for the Airy process, which is the limiting process for a polynuclear growth model. The Airy functions themselves are given by integrals in which the exponents have a…

Consider two ancestral lineages sampled from a system of two-dimensional branching random walks with logistic regulation in the stationary regime. We study the asymptotics of their coalescence time for large initial separation and find that…

We present new combinatorial and probabilistic identities relating three random processes: the oriented swap process on $n$ particles, the corner growth process, and the last passage percolation model. We prove one of the probabilistic…

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 consider last-passage percolation models in two dimensions, in which the underlying weight distribution has a heavy tail of index alpha<2. We prove scaling laws and asymptotic distributions, both for the passage times and for the shape…