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6 papers · 2 filters
A Lamperti-type representation of continuous-state branching processes with immigration
M. Emilia Caballero, José Luis Pérez Garmendia, Gerónimo Uribe Bravo
Guided by the relationship between the breadth-first walk of a rooted tree and its sequence of generation sizes, we are able to include immigration in the Lamperti representation o…
Strict inequalities of critical values in continuum percolation
Massimo Franceschetti, Mathew D. Penrose, Tom Rosoman
We consider the supercritical finite-range random connection model where the points of a homogeneous planar Poisson process are connected with probability for a gi…
Random networks with sublinear preferential attachment: The giant component
Steffen Dereich, Peter Mörters
We study a dynamical random network model in which at every construction step a new vertex is introduced and attached to every existing vertex independently with a probability prop…
Local central limit theorems in stochastic geometry
Mathew D. Penrose, Yuval Peres
We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local cent…
From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage
Stefan Adams, Nicolas Dirr, Mark Peletier +1
We study the connection between a system of many independent Brownian particles on one hand and the deterministic diffusion equation on the other. For a fixed time step , a la…
The unscaled paths of branching Brownian motion
Simon C. Harris, Matthew I. Roberts
For a set , we give new results on the growth of the number of particles in a dyadic branching Brownian motion whose paths fall within A. We show that it is p…