Related papers: A continuum individual based model of fragmentatio…
We construct a class of discontinuous superprocesses with dependent spatial motion and general branching mechanism. The process arises as the weak limit of critical interacting-branching particle systems where the spatial motions of the…
We determine filtering and master equations for a quantum system interacting with wave packet of light in a continuous-mode squeezed number state. We formulate the problem of conditional evolution of a quantum system making use of model of…
A selfconsistent system of equations describing evolution of linear spherically symmetric perturbations in Fridmann world by an arbitrary equation of state is obtained. The perturbations singular part corresponding to massive particle-like…
The evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements shows versatile behavior, with connections to phase transitions and complexity theory. We reformulate the problem in terms…
We demonstrate how direct simulation of stochastic, individual-based models can be combined with continuum numerical analysis techniques to study the dynamics of evolving diseases. % Sidestepping the necessity of obtaining explicit…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
A continuum individual-based model of hopping and coalescing particles is introduced and studied. Its microscopic dynamics are described by a hierarchy of evolution equations obtained in the paper. Then the passage from the micro- to…
The spreading of entanglement in out-of-equilibrium quantum systems is currently at the centre of intense interdisciplinary research efforts involving communities with interests ranging from holography to quantum information. Here we…
We consider a population of particles with unit life length. Dying each particle produces offspring whose size depends on the random environment specifying the reproduction law of all particles of the given generation and on the number of…
We consider a continuous-time symmetric branching random walk on multidimensional lattices with immigration and infinite number of initial particles. We assume that at every lattice point a process of birth and death of particles is…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
We study existence and uniqueness of the solution to the Vlasov-Poisson system describing a plasma constituted by different species evolving in $\mathbb{R}^3$, whose particles interact via the Coulomb potential. The species can have both…
We present a theoretical study of entanglement in ensembles consisting of an arbitrary number of particles. Multipartite entanglement criteria in terms of observables are formulated for a fixed number of particles as well as for systems…
We consider the behaviour of branching-selection particle systems in the large population limit. The dynamics of these systems is the combination of the following three components: (a) Motion: particles move on the real line according to a…
We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic…
The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain. The simulations of this stochastic process and its invariant measure are…
We consider a particle system on $\mathbb{Z}^d$ with real state space and interactions of infinite range. Assuming that the rate of change is continuous we obtain a Kalikow-type decomposition of the infinite range change rates as a mixture…
We consider systems of particles hopping stochastically on $d$-dimensional lattices with space-dependent probabilities. We map the master equation onto an evolution equation in a Fock space where the dynamics are given by a quantum…
We investigate the statistics of selected rare events in a (1+1)-dimensional (classical) stochastic growth model which describes the evolution of (quantum) random unitary circuits. In such classical formulation, particles are created and/or…
We show that spatial extensions of many-species population dynamics models, such as the Lotka-Volterra model with random interactions we focus on in this work, generically exhibit scale-free correlation functions of population sizes in the…