Related papers: Branching Brownian motion with rank-based selectio…
We consider a branching particle model in which particles move inside a Euclidean domain according to the following rules. The particles move as independent Brownian motions until one of them hits the boundary. This particle is killed but…
We identify the fluctuations of the partition function for a class of random energy models, where the energies are given by the positions of the particles of the complex-valued branching Brownian motion (BBM). Specifically, we provide the…
We construct a planar diffusion process whose infinitesimal generator depends only on the order of the components of the process. Speaking informally and a bit imprecisely for the moment, imagine you run two Brownian-like particles on 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,…
We introduce oscillatory analogues of fractional Brownian motion, sub-fractional Brownian motion and other related long range dependent Gaussian processes, we discuss their properties, and we show how they arise from particle systems with…
We study interacting particle systems on the real line which generalize the Hammersley process [D. Aldous and P. Diaconis, Prob. Theory Relat. Fields 103, 199-213 (1995)]. Particles jump to the right to a randomly chosen point between their…
We develop Random Batch Methods for interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the computational cost is reduced from $O(N^2)$ per time step to…
We study the long-range asymptotic behavior for an out-of-equilibrium countable one-dimensional system of Brownian particles interacting through their rank-dependent drifts. Focusing on the semi-infinite case, where only the leftmost…
We study various combinations of active diffusion with branching, as an extension of standard reaction-diffusion processes. We concentrate on the selection of the asymptotic wavefront speed for thermal run-and-tumble and for thermal active…
The asymptotic behavior of a subcritical Branching Process in Random Environment (BPRE) starting with several particles depends on whether the BPRE is strongly subcritical (SS), intermediate subcritical (IS) or weakly subcritical (WS).…
A general class of non-Markov, supercritical Gaussian branching particle systems is introduced and its long-time asymptotics is studied. Both weak and strong laws of large numbers are developed with the limit object being characterized in…
We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle…
We calculate the probability distribution function (PDF) of an overdamped Brownian particle moving in a periodic potential energy landscape $U(x)$. The PDF is found by solving the corresponding Smoluchowski diffusion equation. We derive the…
In this note, we recall the definition of the binary branching model with Moran type interactions (BBMMI) introduced in [8]. In this interacting particle system, particles evolve, reproduce and die independently and, with a probability that…
Consider branching Brownian motion with absorption in which particles move independently as one-dimensional Brownian motions with drift $-\rho$, each particle splits into two particles at rate one, and particles are killed when they reach…
A $d$-dimensional branching diffusion, $Z$, is investigated, where the linear attraction or repulsion between particles is competing with an Ornstein-Uhlenbeck drift, with parameter $b$ (we take $b>0$ for inward O-U and $b<0$ for outward…
The paper addresses Brownian motion in the logarithmic potential with time-dependent strength, $U(x,t) = g(t) \log(x)$, subject to the absorbing boundary at the origin of coordinates. Such model can represent kinetics of…
We derive asymptotics for the quenched probability that a critical branching Brownian motion killed at a small rate in Poissonian obstacles exits a large domain. Results are formulated in terms of the solution to a semilinear partial…
We consider inhomogeneous branching diffusions on an infinite domain of $\mathbb{R}^d$. The first aim of this article is to derive a general criterium under which the size process (number of particles) and the genealogy of the particle…
The Fleming-Viot particle system consists of $N$ identical particles diffusing in a domain $U \subset \mathbb{R}^d$. Whenever a particle hits the boundary $\partial U$, that particle jumps onto another particle in the interior. It is known…