Related papers: A generating function approach to branching random…
We investigate a branching random walk where the displacements are independent from the branching mechanism and have a stretched exponential distribution. We describe the positions of the particles in the vicinity of the rightmost particle…
Using the annealed approach we investigate the asymptotic behavior of the survival probability of a critical multitype branching process evolving in i.i.d. random environment. We show under rather general assumptions on the form of the…
The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…
Locally activated random walks are defined as random processes, whose dynamical parameters are modified upon visits to given activation sites. Such dynamics naturally emerge in living systems as varied as immune and cancer cells interacting…
The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov branching process, which can…
We introduce a population dynamics model, where individual genomes are represented by bit-strings. Selection is described by death probabilities which depend on these genomes, and new individuals continuously replace the ones that die,…
We study a branching-process random iterated function system (RIFS) defined by a recursive replacement of leaves by finite subtrees at strictly smaller contraction scales. This construction yields a tree-valued, infinite-depth random…
We consider random walks in dynamic random environments which arise naturally as spatial embeddings of ancestral lineages in spatial locally regulated population models. In particular, as the main result, we prove the quenched central limit…
We study a universal object for the genealogy of a sample in populations with mutations: the critical birth-death process with Poissonian mutations, conditioned on its population size at a fixed time horizon. We show how this process arises…
Branching random walks are key to the description of several physical and biological systems, such as neutron multiplication, genetics and population dynamics. For a broad class of such processes, in this Letter we derive the discrete…
Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…
We consider the branching random walk in random environment with a random absorption wall. When we add this barrier, we discuss some topics related to the survival probability. We assume that the random environment is i.i.d., $S_i$ is a…
We introduce a broad class of families of branching random walks on a set $X$. The processes in each family are parametrized by a positive parameter $\lambda$ and they are monotonically increasing in $\lambda$ with respect to the germ…
We study a branching random walk on $\r$ with an absorbing barrier. The position of the barrier depends on the generation. In each generation, only the individuals born below the barrier survive and reproduce. Given a reproduction law,…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
By using the matrix formulation of the two-step approach to distributions of patterns in random sequences, recurrence and explicit formulas for the generating functions of successions in random permutations of arbitrary multisets are…
We study the elephant random walk in arbitrary dimension $d\geq 1$. Our main focus is the limiting random variable appearing in the superdiffusive regime. Building on a link between the elephant random walk and P\'olya-type urn models, we…
Bernoulli random walks, a simple avalanche model, and a special branching process are essesntially identical. The identity gives alternative insights into the properties of these basic model sytems.
We consider stochastic processes indexed by the vertices of an infinite binary tree having a simple recursive structure. The value at any vertex is some fixed function of the values at the two daughter vertices together with some…
We consider the limiting behaviour of the point processes associated with a branching random walk with supercritical branching mechanism and balanced regularly varying step size. Assuming that the underlying branching process satisfies…