Related papers: On multitype Branching Processes with Interaction
We consider a stochastic individual-based population model with competition, trait-structure affecting reproduction and survival, and changing environment. The changes of traits are described by jump processes, and the dynamics can be…
We investigate the genealogical structure of general critical or subcritical continuous-state branching processes. Analogously to the coding of a discrete tree by its contour function, this genealogical structure is coded by a real-valued…
Branching-stable processes have recently appeared as counterparts of stable subordinators, when addition of real variables is replaced by branching mechanism for point processes. Here, we are interested in their domains of attraction and…
The goal of this paper is to develop a theory of graphon-valued stochastic processes, and to construct and analyse a natural class of such processes arising from population genetics. We consider finite populations where individuals change…
By considering the master equation of asymmetric exclusion process on a one-dimensional lattice, we obtain the most general boundary condition of the multi-species exclusion processes in which the number of particles is constant in time.…
The dynamics of diffusion in complex networks are widely studied to understand how entities, such as information, diseases, or behaviors, spread in an interconnected environment. Complex networks often present community structure, and tools…
We introduce an interacting particle system that models the spread of an epidemic in terms of heterogeneous diffusive dynamics, rather than exogenous contact and transmission rates at the population level as in classical compartmental…
We explore a generalized Seceder Model with variable size selection groups and higher dimensional genotypes, uncovering its well-defined mean-field limiting behavior. Mapping to a discrete, deterministic version, we pin down the upper…
We define a new stochastic process on general simplicial complexes which allows to study their spectral and homological properties. Some results for random walks on graphs are shown to hold in this general setting. As an application, the…
We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
This paper generalizes the strong seed-bank model introduced in arXiv:1411.4747 to allow for more general dormancy time distributions, such as a type of Pareto distribution. Inspired by the method of approximation using models with…
We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…
This paper is a collection of recent results on discrete-time and continuous-time branching random walks. Some results are new and others are known. Many aspects of this theory are considered: local, global and strong local survival, the…
It is well understood that a supercritical continuous-state branching process (CSBP) is equal in law to a discrete continuous-time Galton Watson process (the skeleton of prolific individuals) whose edges are dressed in a Poissonian way with…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
We investigate the well-posedness and asymptotic self-similarity of solutions to a generalized Smoluchowski coagulation equation recently introduced by Bertoin and Le Gall in the context of continuous-state branching theory. In particular,…
Representations of branching Markov processes and their measure-valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a "level,"…
In this paper we study general nonlinear stochastic differential equations, where the usual Brownian motion is replaced by a L\'evy process. We also suppose that the coefficient multiplying the increments of this process is merely Lipschitz…
This paper continues the research project launched in [Constr. Approx. (2025) https://doi.org/10.1007/s00365-023-09675-9] and aimed at studying time-inhomogeneous one-dimensional branching processes (mainly on a continuous but also on a…