Related papers: Balanced two-type annihilation: mean-field asympto…
The dynamical mechanisms that can stabilize the coexistence of species (or strategies) are of substantial interest for the maintenance of biodiversity and in sociobehavioural dynamics. We investigate the mean extinction time in the…
We study a generalized discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic…
A mean field spin system consisting two interacting groups each with homogeneous interaction coefficients is introduced and studied. Existence of the thermodynamic limit is shown by an asymptotic sub-addittivity method and factorization of…
In this paper we introduce and discuss kinetic equations for the evolution of the probability distribution of the number of particles in a population subject to binary interactions. The microscopic binary law of interaction is assumed to be…
We investigate consensus formation and the asymptotic consensus times in stylized individual- or agent-based models, in which global agreement is achieved through pairwise negotiations with or without a bias. Considering a class of…
We consider extinction times for a class of birth-death processes commonly found in applications, where there is a control parameter which determines whether the population quickly becomes extinct, or rather persists for a long time. We…
We investigate extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state n=0 is a repelling…
We consider a Fleming-Viot-type particle system consisting of independently moving particles that are killed on the boundary of a domain. At the time of death of a particle, another particle branches. If there are only two particles and the…
We analyze a two-offspring Branching Annihilating Random Walk ($n=2$ BAW) model, with finite annihilation rate. The finite annihilation rate allows for a dynamical phase transition between a vacuum, absorbing state and a non-empty, active…
We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. A law of large numbers result is established as…
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…
Action-detected two-dimensional (2D) spectroscopy resolves the time-dependent nonlinear optical response of a quantum system by recording incoherently detected observables such as fluorescence, photoelectrons, or photocurrents which reflect…
In the long run, the eventual extinction of any biological population is an inevitable outcome. While extensive research has focused on the average time it takes for a population to go extinct under various circumstances, there has been…
We study a simple one-dimensional model of ballisticaly-controlled annihilation in which the two annihilating species are initially spatially separated. The time dependent properties of the annihilation front are exactly derived. It is…
We study a system consisting of $n$ particles, moving forward in jumps on the real line. Each particle can make both independent jumps, whose sizes have some distribution, or ``synchronization'' jumps, which allow it to join a randomly…
This note gives an exponential tail approximation for the extinction time of a subcritical multitype branching process arising from the SIR epidemic model on a random graph with given degrees, where the type corresponds to the vertex…
We consider critical branching Brownian motion with absorption, in which there is initially a single particle at $x > 0$, particles move according to independent one-dimensional Brownian motions with the critical drift of $-\sqrt{2}$, and…
We study inhomogeneous host-pathogen dynamics to model the global amphibian population extinction in a lake basin system. The lake basin system is modeled as quenched disorder. In this model we show that once the pathogen arrives at the…
We consider a branching Brownian motion which starts from $0$ with drift $\mu \in \mathbb{R}$ and we focus on the number $Z_x$ of particles killed at $-x$, where $x>0$. Let us call $\mu_0$ the critical drift such that there is a positive…
We consider a system of particles experiencing diffusion and mean field interaction, and study its behaviour when the number of particles goes to infinity. We derive non-asymptotic large deviation bounds measuring the concentration of the…