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Upon almost-every realisation of the Brownian continuum random tree (CRT), it is possible to define a canonical diffusion process or `Brownian motion'. The main result of this article establishes that the cover time of the Brownian motion on the Brow
Externí odkaz:
http://arxiv.org/abs/2410.03922
Autor:
Bhat, Ananda Shikhara
Infinitely many distinct trait values may arise in populations bearing quantitative traits, and modelling their population dynamics is thus a formidable task. While classical models assume fixed or infinite population size, models in which the total
Externí odkaz:
http://arxiv.org/abs/2406.10739
We propose a change in focus from the prevalent paradigm based on the branching property as a tool to analyze the structure of population models, to one based on the self-similarity property, which we also introduce for the first time in the setting
Externí odkaz:
http://arxiv.org/abs/2405.10193
We study the thick points of branching Brownian motion and branching random walk with a critical branching mechanism, focusing on the critical dimension $d = 4$. We determine the exponent governing the probability to hit a small ball with an exceptio
Externí odkaz:
http://arxiv.org/abs/2312.00711
Autor:
Hong, Jieliang, Mytnik, Leonid
For a Dawson-Watanabe superprocess $X$ on $\mathbb{R}^d$, it is shown in Perkins (1990) that if the underlying spatial motion belongs to a certain class of L\'evy processes that admit jumps, then with probability one the closed support of $X_t$ is th
Externí odkaz:
http://arxiv.org/abs/2311.13757
In this paper we consider stochastic processes taking values in a set of continuum graphs we call graphemes, defined as equivalence classes of sequences of vertices labelled by N embedded in an uncountable Polish space (with the cardinality of the co
Externí odkaz:
http://arxiv.org/abs/2311.00173
Autor:
Gall, Jean-François Le, Perkins, Edwin
We show that local times of super-Brownian motion, or of Brownian motion indexed by the Brownian tree, satisfy an explicit stochastic differential equation. Our proofs rely on both excursion theory for the Brownian snake and tools from the theory of
Externí odkaz:
http://arxiv.org/abs/2309.06899
In [Athreya, den Hollander, R\"ollin; 2021, arXiv:1908.06241] models from population genetics were used to define stochastic dynamics in the space of graphons arising as continuum limits of dense graphs. In the present paper we exhibit an example of
Externí odkaz:
http://arxiv.org/abs/2308.11598
Autor:
Blath, Jochen, Jacobi, Dave
We introduce and construct on/off super-Brownian motion (on/off SBM) as a measure-valued scaling limit of critical on/off branching Brownian motions. The distinguishing feature of this process is that its infinitesimal particles can switch individual
Externí odkaz:
http://arxiv.org/abs/2307.10968
Let $X^I_n$ be the coalescence time of two particles picked at random from the $n$th generation of a critical Galton-Watson process with immigration, and let $A^I_n$ be the coalescence time of the whole population in the $n$th generation. In this pap
Externí odkaz:
http://arxiv.org/abs/2307.07384