Related papers: Self-repellent branching random walk
We investigate a model of continuous-time simple random walk paths in $\mathbb{Z}^d$ undergoing two competing interactions: an attractive one towards the large values of a random potential, and a self-repellent one in the spirit of the…
We study the statistical properties of the convex hull of a planar run-and-tumble particle (RTP), also known as the "persistent random walk", where the particle/walker runs ballistically between tumble events at which it changes its…
We propose a picture of the fluctuations in branching random walks, which leads to predictions for the distribution of a random variable that characterizes the position of the bulk of the particles. We also interpret the $1/\sqrt{t}$…
In this work, we consider a modification of the usual Branching Random Walk (BRW), where we give certain independent and identically distributed (i.i.d.) displacements to all the particles at the $n$-th generation, which may be different…
We consider a branching random walk in time-inhomogeneous random environment, in which all particles at generation $k$ branch into the same random number of particles $\mathcal{L}_{k+1}\ge 2$, where the $\mathcal{L}_k$, $k\in\mathbb{N}$,…
We study the dynamics of the outliers for a large number of independent Brownian particles in one dimension. We derive the multi-time joint distribution of the position of the rightmost particle, by two different methods. We obtain the two…
We consider the problem of a particle traveling from an initial configuration to a final configuration (given by a point in the plane along with a prescribed velocity vector) in minimum time with non-homogeneous velocity and with…
We consider a general discrete-time branching random walk on a countable set X. We relate local, strong local and global survival with suitable inequalities involving the first-moment matrix M of the process. In particular we prove that,…
We study nearest-neighbors branching random walks started from a point at the interior of a hypercube. We show that the probability that the process escapes the hypercube is monotonically decreasing with respect to the distance of its…
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…
We consider a family of branching-selection particle systems in which particles branch at time dependent rate $r$ and are killed with a probability which is dependent on their rank via some function $\psi$. We show that, under fairly…
We focus on the existence and characterization of the limit for a certain critical branching random walks in time-space random environment in one dimension which was introduced by M. Birnkenr et.al. Each particle performs simple random walk…
We study the transport of self-propelled particles in dynamic complex environments. To obtain exact results, we introduce a model of run-and-tumble particles (RTPs) moving in discrete time on a $d$-dimensional cubic lattice in the presence…
We study two random processes on an $n$-vertex graph inspired by the internal diffusion limited aggregation (IDLA) model. In both processes $n$ particles start from an arbitrary but fixed origin. Each particle performs a simple random walk…
Consider a branching Brownian motion (BBM). It is well known \cite{Bramson1983ConvergenceOS, Lalley1987ACL} that the rightmost particle is located near \( m_t = \sqrt{2} t - \frac{3}{2\sqrt{2}} \log t \). Let $\mathcal{N}(t,x)$ be the set…
An intrinsic branching structure within the transient random walk on a strip in a random environment is revealed. As applications, which enables us to express the hitting time explicitly, and specifies the density of the absolutely…
How much work does it cost for a propelled particle to stay localised near a stationary target, defying both thermal noise and a constant flow that would carry it away? We study the control of such a particle in finite time and find optimal…
We study downward deviations of the maximum local time of the discrete-time simple random walk on $\mathbb{Z}^d$, $d\ge 3$. In our previous paper \cite{li2026ldmaxlocal}, the corresponding upper bound was established, while the matching…
We consider a branching particle system where each particle moves as an independent Brownian motion and breeds at a rate proportional to its distance from the origin raised to the power $p$, for $p\in[0,2)$. The asymptotic behaviour of the…
We consider a continuous-time branching random walk on a multidimensional lattice with two types of particles and an infinite number of initial particles. The main results are devoted to the study of the generating function and the limiting…