Related papers: A Trotter-type approach to infinite rate mutually …
We construct a mutually catalytic branching process on a countable site space with infinite "branching rate". The finite rate mutually catalytic model, in which the rate of branching of one population at a site is proportional to the mass…
Consider the mutually catalytic branching process with finite branching rate $\gamma$. We show that as $\gamma\to\infty$, this process converges in finite-dimensional distributions (in time) to a certain discontinuous process. We give…
The symbiotic branching model describes a spatial population consisting of two types that are allowed to migrate in space and branch locally only if both types are present. We continue our investigation of the large scale behaviour of the…
We study a continuous time Mutually Catalytic Branching model on the $\mathbb{Z}^{d}$. The model describes the behavior of two different populations of particles, performing random walk on the lattice in the presence of branching, that is,…
In several examples, dualities for interacting diffusion and particle systems permit the study of the longtime behavior of solutions. A particularly difficult model in which many techniques collapse is a two-type model with mutually…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…
In this study we formulate a theoretical approach, based on a Boltzmann-like kinetic equation, to describe pattern formation in two-dimensional mixtures of microtubular filaments and molecular motors. Following the previous work by Aranson…
We are interested in the dynamic of a structured branching population where the trait of each individual moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event…
We consider the dynamics $t\mapsto\tau_t$ of an infinite quantum lattice system that is generated by a local interaction. If the interaction decomposes into a finite number of terms that are themselves local interactions, we show that…
The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes…
We model the evolution of two competing populations $U_t, V_t $ by a two-dimensional size-dependent branching process. The population characteristics are assumed to be close to each other, as in a resident-mutant situation. Given that $U_t…
We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities,…
We consider a spatial multi-type branching model in which individuals migrate in geographic space according to random walks and reproduce according to a state-dependent branching mechanism which can be sub-, super- or critical depending on…
We develop a general technique for proving convergence of repeated quantum interactions to the solution of a quantum stochastic differential equation. The wide applicability of the method is illustrated in a variety of examples. Our main…
We study the density fluctuations at equilibrium of the multi-species stirring process, a natural multi-type generalization of the symmetric (partial) exclusion process. In the diffusive scaling limit, the resulting process is a system of…
We discuss a general procedure to construct an integrable real-time trotterization of interacting lattice models. As an illustrative example we consider a spin-$1/2$ chain, with continuous time dynamics described by the isotropic ($XXX$)…
We develop and implement new probabilistic strategy for proving basic results about long time behaviour for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process as…
In this work we model the dynamics of a population that evolves as a continuous time branching process with a trait structure and ecological interactions in form of mutations and competition between individuals. We generalize existing…
Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely…
The paper analyses stochastic systems describing reacting molecular systems with a combination of two types of state spaces, a finite-dimensional, and an infinite dimenional part. As a typical situation consider the interaction of larger…