Related papers: A non-oriented first passage percolation model and…
We study intersection properties of two or more independent tree-like random graphs. Our setting encompasses critical, possibly long range, Bernoulli percolation clusters, incipient infinite clusters, as well as critical branching random…
Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are…
Recently, many results have been established drawing a parallel between Bernoulli percolation and models given by levels of smooth Gaussian fields with unbounded, strongly decaying correlation. In a previous work with D. Gayet , we started…
We introduce a new first passage percolation model in a Poissonian environment on $\mathbb{R}^{2}$. In this model, the action of a path depends on the geometry of the path and the travel time. We prove that the transversal fluctuation…
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 define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This invariance stems from a reversibility property of the model.…
Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by…
We study continuous-time (variable speed) random walks in random environments on $\mathbb{Z}^d$, $d\ge2$, where, at time $t$, the walk at $x$ jumps across edge $(x,y)$ at time-dependent rate $a_t(x,y)$. The rates, which we assume stationary…
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 variable-speed random walks on $\mathbb Z$ driven by a family of nearest-neighbor time-dependent random conductances $\{a_t(x,x+1)\colon x\in\mathbb Z, t\ge0\}$ whose law is assumed invariant and ergodic under space-time shifts. We…
We study the shape fluctuation in the first passage percolation on $\mathbb{Z}^d$. It is known that it diverges when the distribution obeys Bernoulli in [Yu Zhang. The divergence of fluctuations for shape in first passage percolation.…
We introduce and study a class of abstract continuous action minimization problems that generalize continuous first and last passage percolation. In this class of models a limit shape exists. Our main result provides a framework under which…
We study competing first passage percolation on graphs generated by the configuration model with infinite-mean degrees. Initially, two uniformly chosen vertices are infected with type 1 and type 2 infection, respectively, and the infection…
We study biased random walks on dynamical percolation on $\mathbb{Z}^d$. We establish a law of large numbers and an invariance principle for the random walk using regeneration times. Moreover, we verify that the Einstein relation holds, and…
One model of real-life spreading processes is First Passage Percolation (also called SI model) on random graphs. Social interactions often follow bursty patterns, which are usually modelled with i.i.d.~heavy-tailed passage times on edges.…
We consider the standard first passage percolation model on $\mathbb Z^d$ with bounded and bounded away from zero weights. We show that the rescaled passage time $\widetilde{\mathbf T}_{n,X}$ restricted to a compact set $X$ satisfies a…
To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime (the first passage time) of a system. The statistical distributions that can be obtained out of the mesoscopic description…
We consider a bivariate diffusion process and we study the first passage time of one component through a boundary. We prove that its probability density is the unique solution of a new integral equation and we propose a numerical algorithm…
We consider the Bernoulli first-passage percolation on $\mathbb Z^d (d\ge 2)$. That is, the edge passage time is taken independently to be 1 with probability $1-p$ and 0 otherwise. Let ${\mu(p)}$ be the time constant. We prove in this paper…
We prove an invariance principle for continuous-time random walks in a dynamically averaging environment on $\mathbb Z$. In the beginning, the conductances may fluctuate substantially, but we assume that as time proceeds, the fluctuations…