Zobrazeno 1 - 10
of 3 334
pro vyhledávání: '"60J80"'
In this survey, we explore the connections between two areas of probability: percolation theory and population genetic models. Our first goal is to highlight a construction on Galton-Watson trees, which has been described in two different ways: Berno
Externí odkaz:
http://arxiv.org/abs/2411.09621
Autor:
Zhiyanov, A. P., Shklyaev, A. V.
We consider a critical bisexual branching process in a random environment generated by independent and identically distributed random variables. Assuming that the process starts with a large number of pairs $N$, we prove that its extinction time is o
Externí odkaz:
http://arxiv.org/abs/2411.07737
Autor:
Gwynne, Ewain, Liu, Jiaqi
It is well-known that conditioning a supercritical (multi-type) branching process on the event that it eventually becomes extinct yields a subcritical branching process. We study the corresponding inverse problem: given a subcritical branching proces
Externí odkaz:
http://arxiv.org/abs/2411.06301
This paper investigates, via methods from the theory of probability on trees, critical phenomena in stochastic cascade models of Yule type, and applies these methods to the problem of uniqueness and nonuniqueness of solutions of particular mean flow
Externí odkaz:
http://arxiv.org/abs/2411.00629
Autor:
Iyer, Tejas
A sequence of trees $(\mathcal{T}_{n})_{n \in \mathbb{N}}$ contains a \emph{persistent hub}, or displays \emph{degree centrality}, if there is a fixed node of maximal degree for all sufficiently large $n \in \mathbb{N}$. We derive sufficient criteria
Externí odkaz:
http://arxiv.org/abs/2410.24170
We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one. The first
Externí odkaz:
http://arxiv.org/abs/2410.20889
In this work, we study a two-type critical branching particle system in $\mathbb{R}^{N}$, where particles follow symmetric stable motions, with type-dependent lifetimes and offspring distributions. Our main result is the convergence as $t\to\infty$ o
Externí odkaz:
http://arxiv.org/abs/2410.17369
Autor:
Kataria, K. K., Vishwakarma, P.
We study a fractional birth-death process with state dependent birth and death rates. It is defined using a system of fractional differential equations that generalizes the classical birth-death process introduced by Feller (1939). We obtain the clos
Externí odkaz:
http://arxiv.org/abs/2410.17344
We present a method of solving a nonlinear Dirichlet problem with discontinuous boundary data and we give a probabilistic representation of the solution using the nonlocal branching process associated with the nonlinear term of the operator. Instead
Externí odkaz:
http://arxiv.org/abs/2410.16988
Autor:
Hinz, Michael, Pachon, Angelica
We study a random graph model with preferential edge attachment and detachment through the embedding into a generalized Yule model. We show that the in-degree distribution of a vertex chosen uniformly at random follows a power law in the supercritica
Externí odkaz:
http://arxiv.org/abs/2410.09974