4 citations · 4 across the 9 of their papers we have counts for
14 papers
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 descenda…
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…
Scaling limit of the Aldous-Broder chain on regular graphs: the transient regime
Osvaldo Angtuncio Hernández, Gabriel Berzunza Ojeda, Anita Winter
The continuum random tree is the scaling limit of the uniform spanning tree on the complete graph with vertices. The Aldous-Broder chain on a graph is a discrete-time…
On the speed of coming down from infinity for subcritical branching processes with pairwise interactions
Gabriel Berzunza Ojeda, Juan Carlos Pardo
In this paper, we study the phenomenon of coming down from infinity for subcritical cooperative branching processes with pairwise interactions (BPI processes) under suitable condit…
Fringe trees for random trees with given vertex degrees
Gabriel Berzunza Ojeda, Cecilia Holmgren, Svante Janson
We prove asymptotic normality for the number of fringe subtrees isomorphic to any given tree in uniformly random trees with given vertex degrees. As applications, we also prove cor…
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 Win…
Convergence of trees with a given degree sequence and of their associated laminations
Gabriel Berzunza Ojeda, Cecilia Holmgren, Paul Thévenin
In this paper, we study uniform rooted plane trees with given degree sequence. We show, under some natural hypotheses on the degree sequence, that these trees converge toward the s…
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,…
Branching processes with pairwise interactions
Gabriel Berzunza Ojeda, Juan Carlos Pardo
In this manuscript, we are interested in the long-term behaviour of branching processes with pairwise interactions (BPI-processes). A process in this class behaves as a pure branch…
The distance profile of rooted and unrooted simply generated trees
Gabriel Berzunza Ojeda, Svante Janson
It is well-known that the height profile of a critical conditioned Galton-Watson tree with finite offspring variance converges, after a suitable normalization, to the local time of…
The -cut model in deterministic and random trees
Gabriel Berzunza, Xing Shi Cai, Cecilia Holmgren
The -cut number of rooted graphs was introduced by Cai et al. as a generalization of the classical cutting model by Meir and Moon. In this paper, we show that all moments of the…
The cut-tree of large trees with small heights
Gabriel Berzunza
We destroy a finite tree of size by cutting its edges one after the other and in uniform random order. Informally, the associated cut-tree describes the genealogy of the connec…