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We consider a branching-selection particle system on $\Z$ with $N \geq 1$ particles. During a branching step, each particle is replaced by two new particles, whose positions are shifted from that of the original particle by independently…
The extreme value statistics of active matter offer significant insight into their unique properties. A phase transition has recently been reported in a model of branching run-and-tumble particles, describing the spatial spreading of an…
We investigate a model in which an ensemble of chemically identical Brownian particles are continuously growing by condensation and at the same time undergo irreversible aggregation whenever two particles come into contact upon collision.…
Let $R:(0,\infty) \to [0,\infty)$ be a measurable function. Consider coalescing Brownian motions started from every point in the subset $\{ (0,x) : x \in \mathbb{R} \}$ of $[0,\infty) \times \mathbb{R}$ (with $[0,\infty)$ denoting time and…
The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in $d \ge 2$ dimensions. Salient features of the phase diagram are established in each case. The models are based on site…
Arratia, and later T\'oth and Werner, constructed random processes that formally correspond to coalescing one-dimensional Brownian motions starting from every space-time point. We extend their work by constructing and characterizing what we…
A class of interacting particle systems on $\mathbb{Z}$, involving instantaneously annihilating or coalescing nearest neighbour random walks, are shown to be Pfaffan point processes for all deterministic initial conditions. As diffusion…
We study the dynamical aspects of the top rank statistics of particles, performing Brownian motions on a half-line, which are ranked by their distance from the origin. For this purpose, we introduce an observable that we call the overlap…
We consider critical branching Brownian motion with absorption, in which there is initially a single particle at $x > 0$, particles move according to independent one-dimensional Brownian motions with the critical drift of $-\sqrt{2}$, and…
We propose a model of run-and-tumble particles (RTPs) on a line with a fertile site at the origin. After going through the fertile site, a run-and-tumble particle gives rise to new particles until it flips direction. The process of creation…
We consider a model of fragmentation of sheet by cracks that move with a velocity in preferred direction, but undergo random transverse displacements as they move. There is a non-zero probability of crack-splitting, and the split cracks…
We investigate the problem of ballistically controlled reactions where particles either annihilate upon collision with probability $p$, or undergo an elastic shock with probability $1-p$. Restricting to homogeneous systems, we provide in…
In this work we introduce a new type of urn model with infinite but countable many colors indexed by an appropriate infinite set. We mainly consider the indexing set of colors to be the $d$-dimensional integer lattice and consider balanced…
We consider one-dimensional activated random walk (ARW) on $\mathbb{Z}$ started from a `point source' initial condition, with many particles at the origin and no other particles. We prove that, uniformly throughout a macroscopic window…
We consider a random model of diffusion and coagulation. A large number of small particles are randomly scattered at an initial time. Each particle has some integer mass and moves in a Brownian motion whose diffusion rate is determined by…
We provide a decomposition of the trace of the Brownian motion into a simple path and an independent Brownian soup of loops that intersect the simple path. More precisely, we prove that any subsequential scaling limit of the loop erased…
The transport of active particles may occur in complex environments, in which it emerges from the interplay between the mobility of the active components and the quenched disorder of the environment. Here we explore structural and dynamical…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
We consider the following interacting particle system: There is a ``gas'' of particles, each of which performs a continuous time simple random walk on the d-dimensional lattice. These particles are called A-particles and move independently…
We present an approximation to the Brunet--Derrida model of supercritical branching Brownian motion on the real line with selection of the $N$ right-most particles, valid when the population size $N$ is large. It consists of introducing a…