Related papers: Quasistationarity and extinction for population pr…

Predicting the long-lasting quasistationary state for a given initial state is one of central issues in Hamiltonian systems having long-range interaction. A recently proposed method is based on the Vlasov description and uniformly…

We study solutions to the evolution equation $u_t=\Delta u-u +\sum_{k\geqslant 1}q_ku^k$, $t>0$, in $\mathbf{R}^d$. Here the coefficients $q_k\geqslant 0$ verify $ \sum_{k\geqslant 1}q_k=1< \sum_{k\geqslant 1}kq_k<\infty$. First, we deal…

In a view for a simple model where natural selection at the individual level is confronted to selection effects at the group level, we consider some individual-based models of some large population subdivided into a large number of groups.…

Epidemic processes on random graphs or networks are marked by localization of activity that can trap the dynamics into a metastable state, confined to a subextensive part of the network, before visiting an absorbing configuration.…

We apply the operator approach to a stochastic system belonging to a class of death-birth processes, which we introduce utilizing the master equation approach. By employing Doi- Peliti formalism we recast the master equation in the form of…

For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…

We develop a spectral formulation and a stationary WKB approximation for calculating the probabilities of rare events (large deviations from the mean) in systems of reacting particles with infinite-range interaction, describable by a master…

We develop a quasilinear theory of the Vlasov equation in order to describe the approach of systems with long-range interactions to quasi-stationary states. We derive a diffusion equation governing the evolution of the velocity distribution…

Given a birth-death process on $\mathbb {N}$ with semigroup $(P_t)_{t\geq0}$ and a discrete gradient ${\partial}_u$ depending on a positive weight $u$, we establish intertwining relations of the form ${\partial}_uP_t=Q_t\,{\partial}_u$,…

We study the two-species diffusion-annihilation process, $A+B\rightarrow$ \O, on the fully-connected lattice. Probability distributions for the number of particles and the reaction time are obtained for a finite-size system using a master…

In this paper we derive a constrained Hamilton-Jacobi equation with obstacle from a discrete non-linear integro-differential model of population dynamics, with exponentially decaying mutation kernel. The exponential decay of the kernel…

Many types of bacteria can survive under stress by switching stochastically between two different phenotypes: the "normals" who multiply fast, but are vulnerable to stress, and the "persisters" who hardly multiply, but are resilient to…

We consider an irreducible pure jump Markov process with rates Q=(q(x,y)) on \Lambda\cup\{0\} with \Lambda countable and 0 an absorbing state. A quasi-stationary distribution (qsd) is a probability measure \nu on \Lambda that satisfies:…

Using the Hamilton-Jacobi method, we solve chemical Fokker-Planck equations within the Gaussian approximation and obtain a simple and compact formula for a conditional probability distribution. The formula holds in general transient…

We study a stochastic version of the classical Becker-D\"oring model, a well-known kinetic model for cluster formation that predicts the existence of a long-lived metastable state before a thermodynamically unfavorable nucleation occurs,…

Hamiltonian systems with long-range interactions give rise to long lived out of equilibrium macroscopic states, so-called quasi-stationary states. We show here that, in a suitably generalized form, this result remains valid for many such…

We use a Hamiltonian dynamics to discuss the statistical mechanics of long-lasting quasi-stationary states particularly relevant for long-range interacting systems. Despite the presence of an anomalous single-particle velocity distribution,…

We study large fluctuations in evolutionary games belonging to the coordination and anti-coordination classes. The dynamics of these games, modeling cooperation dilemmas, is characterized by a coexistence fixed point separating two…

In this paper we develop an analogue of Hamilton-Jacobi theory for the time-evolution operator of a quantum many-particle system. The theory offers a useful approach to develop approximations to the time-evolution operator, and also…

We introduce and study the basic properties of two ergodic stochastic control problems associated with the quasistationary distribution (QSD) of a diffusion process $X$ relative to a bounded domain. The two problems are in some sense dual,…