Related papers: Pemantle's min-plus binary tree
We consider a branching random walk in the non-boundary case where the additive martingale $W_n$ converges a.s. and in mean to some non-degenerate limit $W_\infty$. We first establish the joint tail distribution of $W_\infty$ and the global…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…
A binary system of classical charged particles interacting through a dipole repulsive potential and confined in a two-dimensional hardwall trap is studied by Brownian dynamics simulations. We found that the presence of small particles…
Systems of stochastic particles evolving in a multi-well energy landscape and attracted to their barycenter is the prototypical example of mean-field process undergoing phase transitions: at low temperature, the corresponding mean-field…
The symbiotic branching model is a spatial population model describing the dynamics of two interacting types that can only branch if both types are present. A classical result for the underlying stochastic partial differential equation…
We consider a (one-dimensional) branching Brownian motion process with a general offspring distribution having at least two moments, and in which all particles have a drift towards the origin where they are immediately absorbed. It is…
The hierarchical scenario of structure formation describes how objects like galaxies and galaxy clusters are formed by mergers of small objects. In this scenario, mergers of galaxies can lead to the formation of massive black hole (MBH)…
We explore the effects of dynamical evolution in dense clusters on the companion mass ratio distribution (CMRD) of binary stars. Binary systems are destroyed by interactions with other stars in the cluster, lowering the total binary…
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…
In this paper, the second in a series of two, we justify two important assumptions on which the result is based that in course of a galaxy merger the slingshot ejection of bound stars is sufficiently efficient to allow a supermassive black…
Massive stars are often born in triples, where gravitational dynamics and stellar interactions play a crucial role in shaping their evolution. One such pathway includes the merger of the inner binary, transforming the system to a binary…
Consider a finite system of competing Brownian particles on the real line. Each particle moves as a Brownian motion, with drift and diffusion coefficients depending only on its current rank relative to the other particles. We find a…
We study the joint asymptotic behavior of spacings between particles at the edge of multilevel Dyson Brownian motions, when the number of levels tends to infinity. Despite the global interactions between particles in multilevel Dyson…
Bipartite and global entanglement are analyzed for the ground state of a system of $N$ spin 1/2 particles interacting via a collective spin-spin coupling described by the Lipkin-Meshkov-Glick (LMG) Hamiltonian. Under certain conditions…
We review the theory behind the formation of primordial black hole binaries and their merger rates. We consider the binary formation in the early and late Universe, emphasising the former as it gives the dominant contribution of the present…
We consider black holes resulting from binary black hole mergers. By fitting to numerical results we construct analytic formulas that predict the mass and spin of the final black hole. Our formulas are valid for arbitrary initial spins and…
A coarsened model for a binary system with limited miscibility of components is proposed; the system is described in terms of structural states in small parts of the material. The material is assumed to have two alternative types of…
A granular system confined in a quasi two-dimensional box that is vertically vibrated can transit to an absorbing state in which all particles bounce vertically in phase with the box, with no horizontal motion. In principle, this state can…
The effect of blocking between different species occurring in one dimension is investigated here numerically in the case of particles following branching and annihilating random walk with two offsprings. It is shown that two-dimensional…
In this paper we study the continuous coagulation and multiple fragmentation equation for the mean-field description of a system of particles taking into account the combined effect of the coagulation and the fragmentation processes in…