Related papers: Fluctuations in first-passage percolation

The non-random fluctuation is one of the central objects in first passage percolation. It was proved in [Shuta Nakajima. Divergence of non-random fluctuation in First Passage Percolation. {\em Electron. Commun. Probab.} 24 (65), 1-13.…

We consider first-passage percolation with positive, stationary-ergodic weights on the square lattice $\mathbb{Z}^d$. Let $T(x)$ be the first-passage time from the origin to a point $x$ in $\mathbb{Z}^d$. The convergence of the scaled…

Consider the first passage percolation model on ${\bf Z}^d$ for $d\geq 2$. In this model we assign independently to each edge the value zero with probability $p$ and the value one with probability $1-p$. We denote by $T({\bf 0}, v)$ 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…

A large and sparse random graph with independent exponentially distributed link weights can be used to model the propagation of messages or diseases in a network with an unknown connectivity structure. In this article we study an extended…

We consider standard first-passage percolation on $\Z^d$. Let $e_1$ be the first coordinate vector. Let $a(n)$ be the expected passage time from the origin to $ne_1$. In this short paper, we note that $a(n)$ is increasing under some strong…

First-passage properties are central to the kinetics of target-search processes. Theoretical approaches so far primarily focused on predicting first-passage statistics for a given process or model. In practice, however, one faces the…

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 consider the first passage percolation model on the square lattice with an edge weight distribution F. In this paper, we consider the number of optimal paths for two points separated by a long distance. We show that there is a phase…

We prove results for first-passage percolation on the configuration model with i.i.d. degrees having finite mean, infinite variance and i.i.d. weights with strictly positive support of the form Y=a+X, where a is a positive constant. We…

The Ornstein-Uhlenbeck process of diffusion in the harmonic potential is re-examined in the context of the first-passage time problem. We investigate this problem to the extent that it has not yet been fully resolved and demonstrate exact…

We consider first-passage percolation on the edges of $\mathbb{Z}^2 \times k,$ namely the slab of width $k$. Each edge is assigned independently a passage time of either 0 (with probability $1-p_c(\mathbb{S}_k)$) or 1 ((with probability…

We consider first-passage percolation with positive, stationary-ergodic weights on the square lattice $\mathbb{Z}^d$. Let $T(x)$ be the first-passage time from the origin to a point $x$ in $\mathbb{Z}^d$. The convergence of the scaled…

We study first-passage percolation in two dimensions, using measures mu on passage times with b:=inf supp(mu) >0 and mu({b})=p \geq p_c, the threshold for oriented percolation. We first show that for each such mu, the boundary of the limit…

The theorem of Dekking and Host regarding tightness around the mean of first passage percolation on the binary tree, from the root to a boundary of a ball, is generalized to a class of graphs which includes all lattices in hyperbolic spaces…

We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical…

We consider a simplified model of first-passage percolation, involving two families of i.i.d. random variables $\{\xi_{ij}\}$ and $\{\eta_{ij}\}$ corresponding to the weights of the horizontal and vertical edges respectively. We obtain an…

We study the mean time for a random walk to traverse between two arbitrary sites of the Erdos-Renyi random graph. We develop an effective medium approximation that predicts that the mean first-passage time between pairs of nodes, as well as…

We prove exponential concentration in i.i.d. first-passage percolation in $Z^d$ for all $d \geq 2$ and general edge-weights $(t_e)$. Precisely, under an exponential moment assumption $E e^{\alpha t_e}< \infty$ for some $\alpha>0$) on the…

First-passage time problems are ubiquitous across many fields of study including transport processes in semiconductors and biological synapses, evolutionary game theory and percolation. Despite their prominence, first-passage time…