8 papers
A tightness criterion for fragmentations
Gabriel Berzunza Ojeda, Cecilia Holmgren, Svante Janson
This note presents a simple criterion for the tightness of stochastic fragmentation processes. Our work is motivated by an application to a fragmentation process derived from delet…
Large fringe trees for random trees with given vertex degrees
Gabriel Berzunza Ojeda, Cecilia Holmgren, Svante Janson
This paper extends the study of fringe trees in random plane trees with a given degree statistic. While previous work established the asymptotic normality of the count of fringe tr…
On the excision of Brownian bridge paths
Gabriel Berzunza Ojeda, Ju-Yi Yen
Path transformations are fundamental to the study of Brownian motion and related stochastic processes, offering elegant constructions of the Brownian bridge, meander, and excursion…
Central limit theorem for supercritical Crump-Mode-Jagers processes counted with non-individual random characteristics
Gabriel Berzunza Ojeda, Harlan Connor
Consider a supercritical Crump-Mode-Jagers process counted with a random characteristic that depends on an individual's life and their descen…
Convergence of the pruning processes of stable Galton-Watson trees
Gabriel Berzunza Ojeda, Anita Winter
Since the work of Aldous and Pitman (1998), several authors have studied the pruning processes of Galton-Watson trees and their continuous analogue Lévy trees. Löhr, Voisin and W…
Invariance principle for fragmentation processes derived from conditioned stable Galton-Watson trees
Gabriel Berzunza Ojeda, Cecilia Holmgren
Aldous, Evans and Pitman (1998) studied the behavior of the fragmentation process derived from deleting the edges of a uniform random tree on labelled vertices. In particular,…