Related papers: First passage percolation in Euclidean space and o…

We consider first-passage percolation (FPP) on the triangular lattice with vertex weights $(t_v)$ whose common distribution function $F$ satisfies $F(0)=1/2$. This is known as the critical case of FPP because large (critical) zero-weight…

We generalize the standard site percolation model on the $d$-dimensional lattice to a model on random tessellations of $\mathbb R^d$. We prove the uniqueness of the infinite cluster by adapting the Burton-Keane argument…

In this paper, we study the maximal edge-traversal time (simply we call maximal weight hereafter) on the optimal paths in the first passage percolation for several edge distributions, including the Pareto and Weibull distributions. It is…

We consider first passage percolation on the Erd\H{o}s--R\'{e}nyi graph with $n$ vertices in which each pair of distinct vertices is connected independently by an edge with probability $\lambda/n$ for some $\lambda>1$. The edges of the…

We consider first passage percolation (FPP) where the vertex weight is given by the exponential of two-dimensional log-correlated Gaussian fields. Our work is motivated by understanding the discrete analog for the random metric associated…

We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…

Let $0<a<b<\infty$ be fixed scalars. Assign independently to each edge in the lattice $\mathbb{Z}^2$ the value $a$ with probability $p$ or the value $b$ with probability $1-p$. For all $u,v\in\mathbb{Z}^2$, let $T(u,v)$ denote the first…

We study the random geometry of first passage percolation on the complete graph equipped with independent and identically distributed edge weights, continuing the program initiated by Bhamidi and van der Hofstad [6]. We describe our results…

We study the time constant $\mu(e_{1})$ in first passage percolation on $\mathbb Z^{d}$ as a function of the dimension. We prove that if the passage times have finite mean, $$\lim_{d \to \infty} \frac{\mu(e_{1}) d}{\log d} = \frac{1}{2a},$$…

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…

In 1999, Zhang proved that, for first passage percolation on the square lattice $\mathbb{Z}^2$ with i.i.d. non-negative edge weights, if the probability that the passage time distribution of an edge $P(t_e = 0) =1/2 $, the critical value…

We consider the standard first passage percolation model in the rescaled graph $\mathbb{Z}^d/n$ for $d\geq 2$, and a domain $\Omega$ of boundary $\Gamma$ in $\mathbb{R}^d$. Let $\Gamma^1$ and $\Gamma^2$ be two disjoint open subsets of…

We consider first passage percolation with i.i.d. weights on edges of the d-dimensional cubic lattice. Under the assumptions that a weight is equal to zero with probability smaller than the critical probability of bond percolation in the…

We establish the scaling limit of the geodesics to the root for the first passage percolation distance on random planar maps. We first describe the scaling limit of the number of faces along the geodesics. This result enables us to compare…

Solving optimization problems leads to elegant and practical solutions in a wide variety of real-world applications. In many of those real-world applications, some of the information required to specify the relevant optimization problem is…

We consider first passage percolation on the configuration model. Once the network has been generated each edge is assigned an i.i.d. weight modeling the passage time of a message along this edge. Then independently two vertices are chosen…

We consider the model of i.i.d. first passage percolation on Z^d, where we associate with the edges of the graph a family of i.i.d. random variables with common distribution G on [0, +$\infty$] (including +$\infty$). Whereas the time…

We investigate the moderate and large deviations in first-passage percolation (FPP) with bounded weights on $\mathbb{Z}^d$ for $d \geq 2$. Write $T(\mathbf{x}, \mathbf{y})$ for the first-passage time and denote by $\mu(\mathbf{u})$ the time…

We study the first passage times of discrete-time branching random walks in ${\mathbb R}^d$ where $d\geq 1$. Here, the genealogy of the particles follows a supercritical Galton-Watson process. We provide asymptotics of the first passage…

For $\xi \geq 0$ and $d \geq 3$, the higher-dimensional Liouville first passage percolation (LFPP) is a random metric on $\epsilon \mathbb{Z}^d$ obtained by reweighting each vertex by $e^{\xi h_\epsilon(x)}$, where $h_\epsilon(x)$ is a…