Related papers: Phase transition for a contact process with random…
We use generating functionals to derive a dynamic mean-field description for generalised Lotka-Volterra systems with higher-order quenched random interactions. We use the resulting single effective species process to determine the stability…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical…
We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different speeds, and may interact, possibly randomly, when they meet.…
We study the dynamical evolution of a system with a phase space consisting of configurations with random energies. The dynamics we use is of Glauber type. It allows for some dynamical evolution ang aging even at very low temperatures,…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
Empirical evidence reveals that contagion processes often occur with competition of simple and complex contagion, meaning that while some agents follow simple contagion, others follow complex contagion. Simple contagion refers to spreading…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
In this paper we study the long term evolution of a continuous time Markov chain formed by two interacting birth-and-death processes. The interaction between the processes is modelled by transition rates which are functions with suitable…
We consider a simple discrete-time Markov chain with values in $[0,\infty)^{Z^d}$. The Markov chain describes various interesting examples such as oriented percolation, directed polymers in random environment, time discretizations of binary…
We study the stationary properties of the two-dimensional pair contact process, a nonequilibrium lattice model exhibiting a phase transition to an absorbing state with an infinite number of configurations. The critical probability and…
This paper deals with the stochastic modeling of a class of heterogeneous population in a random environment, called birth-death-swap. In addition to demographic events, swap events, i.e. moves between subgroups, occur in the population.…
In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at birth of individuals or at a constant…
We study survival and extinction of a long-range infection process on a diluted one-dimensional lattice in discrete time. The infection can spread to distant vertices according to a Pareto distribution, however spreading is also prohibited…
An important characteristic of flocks of birds, school of fish, and many similar assemblies of self-propelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added…
A fundamental goal of microbial ecology is to understand what determines the diversity, stability, and structure of microbial ecosystems. The microbial context poses special conceptual challenges because of the strong mutual influences…
We consider a two species process which evolves in a finite or infinite domain in contact with particles reservoirs at different densities, according to the superposition of a generalised contact process and a rapid-stirring dynamics in the…
We define and study a class of resources allocation processes where $gN$ agents, by repeatedly visiting $N$ resources, try to converge to optimal configuration where each resource is occupied by at most one agent. The process exhibits a…
Stochastic chemical reaction or population dynamics in finite systems often terminates in an absorbing state. Yet in large spatially extended systems, the time to reach species extinction (or fixation) becomes exceedingly long. Tuning…
We study the continuous absorbing-state phase transition in the one-dimensional diffusive epidemic process via mean-field theory and Monte Carlo simulation. In this model, particles of two species (A and B) hop on a lattice and undergo…