Related papers: Subdiffusive concentration in first-passage percol…

We study the problem of coexistence in a two-type competition model governed by first-passage percolation on $\Zd$ or on the infinite cluster in Bernoulli percolation. Actually, we prove for a large class of ergodic stationary passage times…

We consider directed first-passage and last-passage percolation on the nonnegative lattice Z_+^d, d\geq2, with i.i.d. weights at the vertices. Under certain moment conditions on the common distribution of the weights, the limits…

We determine the asymptotic speed of the first-passage percolation process on some ladder-like graphs (or width-2 stretches) when the times associated with different edges are independent and exponentially distributed but not necessarily…

We prove a GUE central limit theorem for random variables with finite fourth moment. We apply this theorem to prove that the directed first and last passage percolation problems in thin rectangles exhibit universal fluctuations given by the…

We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original…

For rotationally invariant first passage percolation (FPP) on the plane, we use a multi-scale argument to prove stretched exponential concentration of the first passage times at the scale of the standard deviation. Our results are proved…

We investigate a novel first-passage percolation model, referred to as the Brochette first-passage percolation model, where the passage times associated with edges lying on the same line are equal. First, we establish a point-to-point…

Evaluating the completion time of a random algorithm or a running stochastic process is a valuable tip not only from a purely theoretical, but also pragmatic point of view. In the formal sense, this kind of a task is specified in terms of…

In i.i.d. exponential last-passage percolation, we describe the joint distribution of Busemann functions, over all edges and over all directions, in terms of a joint last-passage problem in a finite inhomogeneous environment. More…

We apply a variation on the methods of Duminil-Copin, Raoufi, and Tassion to establish a new differential inequality applying to both Bernoulli percolation and the Fortuin-Kasteleyn random cluster model. This differential inequality has a…

Let $E$ be the set of edges of the $d$-dimensional cubic lattice $\mathbb{Z}^d$, with $d\geq2$, and let $t(e),e\in E$, be nonnegative values. The passage time from a vertex $v$ to a vertex $w$ is defined as $\inf_{\pi:v\rightarrow…

We consider the standard model of i.i.d. first passage percolation on Z^d given a distribution G on [0, +$\infty$] (including +$\infty$). We suppose that G({0}) > 1 -- p\_c(d), i.e., the edges of positive passage time are in the subcritical…

For $a>0$ and $b \geq 0$, let $\mathbb{G}_{a,b}$ be the subgraph of $\mathbb{Z}^2$ induced by the vertices between the first coordinate axis and the graph of the function $f = f_{a,b}(u) = a \log (1+u) + b \log(1+\log(1+u))$, $u \geq 0$. It…

We consider first-passage percolation on the class of "high-dimensional" graphs that can be written as an iterated Cartesian product $G\square G \square \dots \square G$ of some base graph $G$ as the number of factors tends to infinity. We…

We consider the first passage percolation model on the square lattice. In this model, $\{t(e): e{an edge of}{\bf Z}^2 \}$ is an independent identically distributed family with a common distribution $F$. We denote by $T({\bf 0}, v)$ the…

We derive a sufficient condition for the existence of a subcritical percolation phase for a wide range of continuum percolation models where each vertex is embedded into Euclidean space according to an iid-marked stationary Poisson point…

We study first-passage percolation on $\mathbb Z ^2$ with independent and identically distributed weights, whose common distribution is uniform on $\{a,b\}$ with $0<a<b<\infty $. Following Ahlberg and De la Riva, we consider the passage…

Let (Xt, t >= 0) be a diffusion process with jumps, sum of a Brownian motion with drift and a compound Poisson process. We consider T_x the first hitting time of a fixed level x > 0 by (Xt, t >= 0). We prove that the law of T_x has a…

We consider the first passage percolation model on $\mathbf{Z}^2$. In this model, we assign independently to each edge $e$ a passage time $t(e)$ with a common distribution $F$. Let $T(u,v)$ be the passage time from $u$ to $v$. In this…

In this paper we study first-passage percolation in the configuration model with empirical degree distribution that follows a power-law with exponent $\tau \in (2,3)$. We assign independent and identically distributed (i.i.d.)\ weights to…