Related papers: Probabilistic approach to a cell growth model
Consider "Frozen Random Walk" on $\mathbb{Z}$: $n$ particles start at the origin. At any discrete time, the leftmost and rightmost $\lfloor{\frac{n}{4}}\rfloor$ particles are "frozen" and do not move. The rest of the particles in the "bulk"…
We define a family of continuous-time branching particle systems on the non-negative real line, called branching subordinators, where particles move as independent subordinators. Each particle can also split (at possibly infinite rate) into…
We aim to understand the evolution of the genetic composition of cancer cell populations. To achieve this, we consider an individual-based model representing a cell population where cells divide, die and mutate along the edges of a finite…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
We consider a continuous-time branching random walk on $\mathbb{Z}$ in a random non homogeneous environment. Particles can walk on the lattice points or disappear with random intensities. The process starts with one particle at initial time…
The rate at which individual bacterial cells grow depends on the concentrations of cellular components such as ribosomes and proteins. These concentrations continuously fluctuate over time and are inherited from mother to daughter cells,…
The Galton--Watson process is the simplest example of a branching process. The relationship between the offspring distribution, and, when the extinction occurs almost surely, the distribution of the total progeny is well known. In this…
1 Sharp prediction of extinction times is needed in biodiversity monitoring and conservation management. 2 The Galton-Watson process is a classical stochastic model for describing population dynamics. Its evolution is like the matrix…
The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles go to infinity. The first part concerns model of biological systems: a model for sympatric…
We investigate properties of the particle distribution near the tip of one-dimensional branching random walks at large times $t$, focusing on unusual realizations in which the rightmost lead particle is very far ahead of its expected…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
Growth-fragmentation processes describe the evolution of systems of cells which grow continuously and fragment suddenly; they are used in models of cell division and protein polymerisation. Typically, we may expect that in the long run, the…
In this article, we focus on Bienaym\'e-Galton-Watson processes with linear-fractional offspring distributions. At a fixed generation, we consider a sample of the individuals alive, drawn in two different ways: either through Bernoulli…
We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically…
A birth-death-move process with mutations is a Markov model for a system of marked particles in interaction, that move over time, with births and deaths. In addition the mark of each particle may also change, which constitutes a mutation.…
We consider a time-continuous branching random walk on a one-dimensional lattice on which there is one center (lattice point) of particle generation, called branching source. The generation of particles in the branching source is described…
We analyze the time evolution describing a quantum source for noninteracting particles, either bosons or fermions. The growth behaviour of the particle number (trace of the density matrix) is investigated, leading to spectral criteria for…
Branching processes are widely used to model the viral epidemic evolution. For more adequate investigation of viral epidemic modelling, we suggest to apply branching processes with transport of particles usually called branching random…
We consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system. This continuous time evolution is interspersed by discrete events that occur at random times and change (reset)…
In the framework of Gibbs statistical theory, the issue of the distribution of particle sizes forming the statistical system and the moments of this distribution are considered. This task is relevant for a wide variety of applications. The…