Related papers: Revisiting Offspring Maxima in Branching Processes
We summarize some of the recent developments which link certain problems in combinatorial theory related to random growth to random matrix theory.
This continues work started in part I on a general branching-within-branching model for host-parasite co-evolution. Here we focus on asymptotic results for relevant processes in the case when parasites survive. In particular, limit theorems…
In this review, we examine the recent progress in saliency prediction and proposed several avenues for future research. In spite of tremendous efforts and huge progress, there is still room for improvement in terms finer-grained analysis of…
We consider the well-known problem of the computation of the (limiting) time-dependent performance characteristics of one-dimensional continuous-time birth and death processes on $\mathbb{Z}$ with time varying and possible state-dependent…
We define the height process for super-critical continuous state branching processes with quadratic branching mechanism. It appears as a projective limit of Brownian motions with positive drift reflected at 0 and a>0 as a goes to infinity.…
Being the max-analogue of $\alpha$-stable stochastic processes, max-stable processes form one of the fundamental classes of stochastic processes. With the arrival of sufficient computational capabilities, they have become a benchmark in the…
Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon…
Branching processes are a class of continuous-time Markov chains (CTMCs) prevalent for modeling stochastic population dynamics in ecology, biology, epidemiology, and many other fields. The transient or finite-time behavior of these systems…
We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth and its remaining lifetime decreases at the unit speed. The models…
In developing brain, axons and dendrites are capable of connecting to each other with high precision. Recent advances in imaging have allowed for the monitoring of axonal, dendritic, and synapse dynamics in vivo. It is observed that the…
Suppose that $(Z_n)_{n\geq0}$ is a supercritical branching process in independent and identically distributed random environment. The right tail function of the scaled growth rate for $(Z_n)_{n\geq0}$ is studied. The upper bounds for…
An overview of the results of new exhaustive computations of gaps between primes in arithmetic progressions is presented. We also give new numerical results for exceptionally large least primes in arithmetic progressions.
We study a continuous time Mutually Catalytic Branching model on the $\mathbb{Z}^{d}$. The model describes the behavior of two different populations of particles, performing random walk on the lattice in the presence of branching, that is,…
Subcritical catalytic branching random walk on d-dimensional lattice is studied. New theorems concerning the asymptotic behavior of distributions of local particles numbers are established. To prove the results different approaches are used…
In the literature, the spine decomposition of branching Markov processes was constructed under the assumption that each individual has at least one child. In this paper, we give a detailed construction of the spine decomposition of general…
We examine the population growth system called Q-processes. This is defined by the Galton-Watson Branching system conditioned on non-extinction of its trajectory in the remote future. In this paper we observe the total progeny up to time…
This article studies the stability of solutions of equilibrium equations arising in so-called resource dependent branching processes. We argue that these new models, building on the model already presented by Bruss (1984 a), refined and…
We consider inhomogeneous branching diffusions on an infinite domain of $\mathbb{R}^d$. The first aim of this article is to derive a general criterium under which the size process (number of particles) and the genealogy of the particle…
A curious connection exists between the theory of optimal stopping for independent random variables, and branching processes. In particular, for the branching process $Z_n$ with offspring distribution $Y$, there exists a random variable $X$…
We construct a flow of continuous time and discrete state branching processes. Some scaling limit theorems for the flow are proved, which lead to the path-valued branching processes and nonlocal branching superprocesses over the positive…