相关论文: Existence, uniqueness and coalescence of directed …

We establish estimates for the coalescence time of semi-infinite directed geodesics in the planar corner growth model with i.i.d. exponential weights. There are four estimates: upper and lower bounds on the probabilities of both fast and…

We study first-passage percolation on Z2, where the edge weights are given by a translation-ergodic distribution, addressing questions related to existence and coalescence of infinite geodesics. Some of these were studied in the late 90's…

This paper gives a self-contained proof of the non-existence of nontrivial bi-infinite geodesics in directed planar last-passage percolation with exponential weights. The techniques used are couplings, coarse graining, and control of…

We show that the Busemann process indexed by tilts in the super-differential of the limit shape exists and is unique in the strong sense in the i.i.d.\ planar corner growth model. This means that every probability space that supports the…

We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable models. In a previous paper we constructed…

We consider planar directed last-passage percolation on the square lattice with general i.i.d. weights and study the geometry of the full set of semi-infinite geodesics in a typical realization of the random environment. The structure of…

The 1+1 dimensional corner growth model with exponential weights is a centrally important exactly solvable model in the Kardar-Parisi-Zhang class of statistical mechanical models. While significant progress has been made on the fluctuations…

We show existence, uniqueness, and directedness properties for infinite geodesics in the FPP model. After giving the fundamental definitions, we describe results by Newman and collaborators giving existence and uniqueness of directed…

In this survey article we consider the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside of the class of exactly solvable models. We show how…

We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside of the class of exactly solvable models. Stationary cocycles are constructed…

Geodesic coalescence, or the tendency of geodesics to merge together, is a hallmark phenomenon observed in a variety of planar random geometries involving a random distortion of the Euclidean metric. As a result of this, the union of…

We prove the existence of semi-infinite geodesics for Brownian last-passage percolation (BLPP). Specifically, on a single event of probability one, there exist semi-infinite geodesics started from every space-time point and traveling in…

We continue the study of infinite geodesics in planar first-passage percolation, pioneered by Newman in the mid 1990s. Building on more recent work of Hoffman, and Damron and Hanson, we develop an ergodic theory for infinite geodesics via…

We study Busemann functions, semi-infinite geodesics, and competition interfaces in the exactly solvable last-passage percolation with inhomogeneous exponential weights. New phenomena concerning geodesics arise due to inhomogeneity. These…

A basic question about the directed landscape is how much of it can be reconstructed simply by knowing the shapes of its geodesics. We prove that the directed landscape can be reconstructed from the shapes of its semi-infinite geodesics. In…

Let us consider Euclidean first-passage percolation on the Poisson-Delaunay triangulation. We prove almost sure coalescence of any two semi-infinite geodesics with the same asymptotic direction. The proof is based on an adapted Burton-Keane…

For first passage percolation (FPP) on integer lattice with i.i.d. passage time distributions, in order to show existence of semi-infinite geodesics along a fixed direction, one requires unproven assumptions on the limiting shape. We…

We consider the Busemann process in planar directed first passage percolation. We extend existing techniques to establish the existence of the process in our setting and determine its distribution in a number of integrable models. As…

The study of Kadar-Parsi-Zhang (KPZ) universality class has been a subject of great interest among mathematicians and physicists over the past three decades. A notably successful approach for analyzing KPZ models is the coupling method,…

In this paper, we initiate the study of backward doubly stochastic differential equations (BDSDEs, for short) with quadratic growth. The existence, comparison, and stability results for one-dimensional BDSDEs are proved when the generator…