Related papers: Branching processes in correlated random environme…
We consider a model of Branching Brownian Motion in which the usual spatially-homogeneous and catalytic branching at a single point are simultaneously present. We establish the almost sure growth rates of population in certain…
We investigate the limit behavior of supercritical multitype branching processes in random environments with linear fractional offspring distributions and show that there exists a phase transition in the behavior of local probabilites of…
We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction and disappearance. In particular, we focus on the case where the individuals are initially prepared at equilibrium within a confined geometry.…
We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We focus…
We analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations) in the presence of an absorbing boundary. An analytically solvable model is presented, in which a dynamical phase-transition occurs…
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d \ge 3$ and the environment is "not too random", then, the total…
We analyze evolutionary dynamics in a confluent, branching cellular population, such as in a growing duct, vasculature, or in a branching microbial colony. We focus on the coarse-grained features of the evolution and build a statistical…
Branching processes are widely used to model the viral epidemic evolution. For more adequate investigation of viral epidemic modelling, we suggest to apply branching processes with transport of particles usually called branching random…
Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We reveal the finite-size scaling law of the survival…
We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the tree, which is a measure of the average number of branches…
Conditions for almost sure extinction are studied in discrete time branching processes with an infinite number of types. It is not assumed that the expected number of children is a bounded function of the parent's type. There might also be…
Spreading from a seed is studied by Monte Carlo simulation on a square lattice with two types of sites affecting the rates of birth and death. These systems exhibit a critical transition between survival and extinction. For time- dependent…
Branched flow governs the transition from ballistic to diffusive motion of waves and conservative particle flows in spatially correlated random or complex environments. It occurs in many physical systems from micrometer to interstellar…
The reproduction speed of a continuous-time branching random walk is proportional to a positive parameter $\lambda$. There is a threshold for $\lambda$, which is called $\lambda_w$, that separates almost sure global extinction from global…
We give new formulas on the total number of born particles in the stable birth-and-assassination process, and prove that it has an heavy-tailed distribution. We also establish that this process is a scaling limit of a process of rumor…
Environmental heterogeneity can drive genetic heterogeneity in expanding populations; mutant strains may emerge that trade overall growth rate for an improved ability to survive in patches that are hostile to the wild type. This…
In this article, we focus on Bienaym\'e-Galton-Watson processes with linear-fractional offspring distributions. At a fixed generation, we consider a sample of the individuals alive, drawn in two different ways: either through Bernoulli…
This paper studies: (i) the long time behaviour of the empirical distribution of age and normalised position of an age dependent critical branching Markov process conditioned on non-extinction; and (ii) the super-process limit of a sequence…
Ancestral inference for branching processes in random environments involves determining the ancestor distribution parameters using the population sizes of descendant generations. In this paper, we introduce a new methodology for ancestral…
We ask the question "when will natural selection on a gene in a spatially structured population cause a detectable trace in the patterns of genetic variation observed in the contemporary population?". We focus on the situation in which…