Continuum graph dynamics via population dynamics: well-posedness, duality and equilibria
A Greven, F Hollander, A Klimovsky… - arXiv preprint arXiv …, 2023 - arxiv.org
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 …
we call graphemes, defined as equivalence classes of sequences of vertices labelled by N …
A generalised spatial branching process with ancestral branching to model the growth of a filamentous fungus
L Kuwata - arXiv preprint arXiv:2409.13627, 2024 - arxiv.org
In this work, we introduce a spatial branching process to model the growth of the mycelial
network of a filamentous fungus. In this model, each filament is described by the position of …
network of a filamentous fungus. In this model, each filament is described by the position of …
Branching Processes--A General Concept
A Greven, T Rippl, PK Glöde - arXiv preprint arXiv:1807.01921, 2018 - arxiv.org
The paper has four goals. First, we want to generalize the classical concept of the branching
property so that it becomes applicable for historical and genealogical processes (using the …
property so that it becomes applicable for historical and genealogical processes (using the …
Branching trees I: Concatenation and infinite divisibility
P Glöde, A Greven, T Rippl - 2019 - projecteuclid.org
The goal of this work is to decompose random populations with a genealogy in subfamilies
of a given degree of kinship and to obtain a notion of infinitely divisible genealogies. We …
of a given degree of kinship and to obtain a notion of infinitely divisible genealogies. We …
Genealogy-valued Feller diffusion
A Depperschmidt, A Greven - arXiv preprint arXiv:1904.02044, 2019 - arxiv.org
We consider the evolution of the genealogy of the population currently alive in a Feller
branching diffusion model. In contrast to the approach via labeled trees in the continuum …
branching diffusion model. In contrast to the approach via labeled trees in the continuum …
Stochastic Evolution of spatial populations: From configurations to genealogies and back
A Greven - arXiv preprint arXiv:1907.06965, 2019 - arxiv.org
The paper reviews the results obtained for spatial population models and the evolution of
the genealogies of these populations during the last decade by the author and his …
the genealogies of these populations during the last decade by the author and his …