Related papers: Chase-escape on the configuration model
Consider a system of $K$ particles moving on the vertex set of a finite connected graph with at most one particle per vertex. If there is one, the particle at $x$ chooses one of the $\hbox{deg} (x)$ neighbors of its location uniformly at…
In this paper, we consider an expanding construction of a distributed control system, which is obtained by adding a new subsystem one after the other, until all $n$ subsystems, where $n \ge 2$, are included in the distributed control…
We study an inhomogeneous sparse random graph on [N] = {1, . . . , N } as introduced in a seminal paper by Bollobas, Janson and Riordan (2007): vertices have a type (here in a compact metric space S), and edges between different vertices…
We study a model of stochastic evolutionary game dynamics in which the probabilities that agents choose suboptimal actions are dependent on payoff consequences. We prove a sample path large deviation principle, characterizing the rate of…
Motivated by biological aspects related to fungus growth, we consider the competition of growth and corrosion. We study a modification of the totally asymmetric exclusion process, including the probabilities of injection $\alpha$ and death…
It has been noticed that when the waiting time distribution exhibits a transition from an intermediate time power law decay to a long-time exponential decay in the continuous time random walk model, a transition from anomalous diffusion to…
Rate-induced tipping is an instability that occurs in a system when its time-dependent rate parameter becomes larger than a threshold value. We investigate a Pearson diffusion process, a diffusion process having solutions staying in a…
We study the escape rate of diffusion process with two approaches. We first give an upper rate function for the diffusion process associated with a symmetric, strongly local regular Dirichlet form. The upper rate function is in terms of the…
We study the factorised steady state of a general class of mass transport models in which mass, a conserved quantity, is transferred stochastically between sites. Condensation in such models is exhibited when above a critical mass density…
We study phase transition and percolation at criticality for three random graph models on the plane, viz., the homogeneous and inhomogeneous enhanced random connection models (RCM) and the Poisson stick model. These models are built on a…
The one-dimensional symmetric exclusion process, the simplest interacting particle process, is a lattice-gas made of particles that hop symmetrically on a discrete line respecting hard-core exclusion. The system is prepared on the infinite…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
A one dimensional disordered particle hopping rate asymmetric exclusion process (ASEP) with open boundaries and a random sequential dynamics is studied analytically. Combining the exact results of the steady states in the pure case with a…
Paired comparison data considered in this paper originate from the comparison of a large number N of individuals in couples. The dataset is a collection of results of contests between two individuals when each of them has faced n opponents,…
The food web is a directed graph in which nodes label species and directed links represent the predation between species. The cascade model generates random food webs. The continuum cascade model is a Poisson approximation of the cascade…
We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this interface has an asymptotic direction with…
In this work, cascading transmission line failures are studied through a dynamical model of the power system operating under fixed conditions. The power grid is modeled as a stochastic dynamical system where first-principles…
Brownian escape is key to a wealth of physico-chemical processes, including polymer folding, and information storage. The frequency of thermally activated energy barrier crossings is assumed to generally decrease exponentially with…
The pursuit-evasion problem is widespread in nature, engineering, and societal applications. It is commonly observed in nature that predators often exhibit faster speeds than their prey but have less agile maneuverability. Over millions of…
This paper defines a new model which incorporates three key ingredients of a large class of wireless communication systems: (1) spatial interactions through interference, (2) dynamics of the queueing type, with users joining and leaving,…