Related papers: The branching Brownian motion seen from its tip
We study a system of branching Brownian motions on $\mathbb R$ with annihilation: at each branching time a new particle is created and the leftmost one is deleted. In [7] it has been studied the case of strictly local creations (the new…
A branching L\'evy process can be seen as the continuous-time version of a branching random walk. It describes a particle system on the real line in which particles move and reproduce independently in a Poissonian manner. Just as for L\'evy…
We revisit the ergodic theorem for the frontier of branching Brownian motion (BBM). Motivated by the proof of Arguin, Bovier, and Kistler \cite{arguin2012ergodic}, we provide a shorter and more direct argument. It relies on two…
We study the asymptotic behaviour of the extremal process of a cascading family of branching Brownian motions. This is a particle system on the real line such that each particle has a type in addition to his position. Particles of type $1$…
We prove a conjecture of Lalley and Sellke [Ann. Probab. 15 (1987)] asserting that the empirical (time-averaged) distribution function of the maximum of branching Brownian motion converges almost surely to a double exponential, or Gumbel,…
We give short proofs of two classical results about the position of the extremal particle in a branching Brownian motion, one concerning the median position and another the almost sure behaviour.
This work is a continuation of the manuscript "the structure of extreme level sets in branching Brownian motion", in which the same authors studied the fine structure of the extreme level sets of branching Brownian motion, namely the sets…
We consider branching Brownian motion in which initially there is one particle at $x$, particles produce a random number of offspring with mean $m+1$ at the time of branching events, and each particle branches at rate $\beta = 1/2m$.…
In this article we establish the magnitude of fluctuations of the extreme particle in the model of binary branching Brownian motion with a single catalytic point at the origin.
We give a probabilistic proof for the emergence of the Stable-$1$ Law for the random fluctuations of the mass of the extremal process of branching Brownian Motion away from its tip. This result was already shown by Mytnik et al. albeit…
We consider a Brownian motion with linear drift that splits at fixed time points into a fixed number of branches, which may depend on the branching point. For this process, which we shall refer to as the Brownian decision tree, we…
We consider the model of branching Brownian motion with a single catalytic point at the origin and binary branching. We establish some fine results for the asymptotic behaviour of the numbers of particles travelling at different speeds and…
Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the…
We study the height of the maximal particle at time $t$ of a one dimensional branching Brownian motion with a space-dependent branching rate. The branching rate is set to zero in finitely many intervals (obstacles) of order $t$. We obtain…
We provide a rigorous derivation of the brownian motion as the limit of a deterministic system of hard-spheres as the number of particles $N$ goes to infinity and their diameter $\varepsilon$ simultaneously goes to $0$, in the fast…
We provide a detailed description of all possible Feller processes on infinite} star graphs with finite number of edges, processes that while away from the graph's center behave like a one-dimensional Brownian motion. The description can be…
Consider a two-type reducible branching Brownian motion in which particles' diffusion coefficients and branching rates are influenced by their types. Here reducible means that type 1 particles can produce particles of type 1 and type 2, but…
We consider a branching Brownian motion with linear drift in which particles are killed on exiting the interval (0,K) and study the evolution of the process on the event of survival as the width of the interval shrinks to the critical value…
We consider a branching-selection system of particles on the real line that evolves according to the following rules: each particle moves according to a Brownian motion during an exponential lifetime and then splits into two new particles…
In this paper, we study branching Brownian motion with absorption, in which particles undergo Brownian motions and are killed upon hitting the absorption barrier. We prove that the empirical distribution function of the maximum of this…