Related papers: First passage percolation and competition models
Counting how many particles pass through a specific space within a specific time is an interesting question in applied physics and social science. Here a logistic model is developed to estimate the total number of flowing particles. This…
First-passage percolation is a random growth model which has a metric structure. An infinite geodesic is an infinite sequence whose all sub-sequences are shortest paths. One of the important quantity is the number of infinite geodesics…
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 [9]. We describe our results…
First passage under restart has recently emerged as a conceptual framework to study various stochastic processes under restart mechanism. Emanating from the canonical diffusion problem by Evans and Majumdar, restart has been shown to…
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…
In this paper we consider an equilibrium last-passage percolation model on an environment given by a compound two-dimensional Poisson process. We prove an $\LL^2$-formula relating the initial measure with the last-passage percolation time.…
We consider a multi-class queueing network as a model of packet transfer in a communication network. We define a second stochastic model as a model document transfer in a communication network where the documents transferred have a general…
We develop a model to compute the first-passage time of a random walker in a crowded environment. Hard-core particles with the same size and diffusion coefficient than the tracer diffuse, and the model allows to compute the first passage…
Aging, the dependence of the dynamics of a physical process on the time $t_a$ since its original preparation, is observed in systems ranging from the motion of charge carriers in amorphous semiconductors over the blinking dynamics of…
We review several competing chaining methods to estimate the supremum, the diameter of the range or the modulus of continuity of a stochastic process in terms of tail bounds of their two-dimensional distributions. Then we show how they can…
We consider the standard first passage percolation model in the rescaled lattice $\mathbb{Z}^d$ for $d\geq 2$ and a bounded domain $\Omega$ in $\mathbb R ^d$. We denote by $\Gamma^1$ and $\Gamma^2$ two disjoint subsets of $\partial \Omega$…
We consider large random planar maps and study the first-passage percolation distance obtained by assigning independent identically distributed lengths to the edges. We consider the cases of quadrangulations and of general planar maps. In…
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…
Fluctuations in stochastic systems are usually characterized by the full counting statistics, which analyzes the distribution of the number of events taking place in the fixed time interval. In an alternative approach, the distribution of…
We study the first-passage time (FPT) problem for widespread recurrent processes in confined though large systems and present a comprehensive framework for characterizing the FPT distribution over many time scales. We find that the FPT…
We consider the first-crossing-time problem through a constant boundary for a Wiener process perturbed by random jumps driven by a counting process. On the base of a sample-path analysis of the jump-diffusion process we obtain explicit…
Splitting probabilities quantify the likelihood of a given outcome out of competitive events. This key observable of random walk theory, historically introduced as the gambler's ruin problem, is well understood for memoryless (Markovian)…
We consider the standard first passage percolation model on Z^d with a distribution G on R+ that admits an exponential moment. We study the maximal flow between a compact convex subset A of R^d and infinity. The study of maximal flow is…
This paper considers the class of L\'evy processes that can be written as a Brownian motion time changed by an independent L\'evy subordinator. Examples in this class include the variance gamma model, the normal inverse Gaussian model, and…
A simple lemma bounds $\mathrm{s.d.}(T)/\mathbb{E} T$ for hitting times $T$ in Markov chains with a certain strong monotonicity property. We show how this lemma may be applied to several increasing set-valued processes. Our main result…