Gabriel Hernán Berzunza Ojeda

University of Liverpool

Department of Mathematical Sciences

Mathematical Sciences Building

L69 7ZL Liverpool

United Kingdom

Email : Gabriel.Berzunza-Ojeda@liverpool.ac.uk

Office : Room 204 

About me

I am a senior lecturer at the Department of Mathematical Sciences of the University of Liverpool. I joined the department in September 2020.

Prior to that:

In 2016, I have obtained my PhD at the Mathematics department of the University of Zurich under the supervision of Jean Bertoin. 

From 2017 to 2018 I went on to the Institut für Mathematische Stochastik of Georg-August-Universität Göttingen, where I held a postdoc position in the research team of Anja Sturm founded by the SPP Priority Programme 1590: Probabilistic Structures in Evolution. 

From 2018 to 2020 I was a postdoc at the Matematiska institutionen of Uppsala Universitet, where I worked with Cecilia Holmgren, founded by the research grant from the Swedish Foundations Starting Grant from Ragnar Söderbergs Foundation, project  "Analysis of random graphs and trees with focus on fringe trees, percolation and random networks".

My general research interest concern combinatorics, probability theory and stochastic processes. My work also intersects with a wide variety of (applied) probability models arising in coalescent-fragmentation theory, Lévy processes, percolation, random trees, random walks and stochastic population models. 

Publications & pre-publications

All the papers are available on arXiv. See below the list in reverse chronological order.

• Convergence of the pruning processes of stable Galton-Watson trees (with A. Winter)
  Submitted, available at arXiv:2304.10489, 2023.
• Fringe trees for random trees with given vertex degrees (with C. Holmgren and S. Janson)
  Submitted, available at arXiv:2312.04243, 2023.
• Invariance principle for fragmentation processes derived from conditioned stable Galton-Watson tree (with C. Holmgren)
  Bernoulli, 29, 2745-2770, 2023.
• The fluctuations of the giant cluster for percolation on random split trees (with X. S. Cai and C. Holmgren)
  Latin American Journal of Probability and Mathematical Statistics (ALEA), 19, 665-700, 2022.
• The asymptotic distribution of cluster sizes for supercritical percolation on random split trees  (with C. Holmgren)
  Random Structures & Algorithms, 60, 631-652, 2022.
• The distance profile of rooted and unrooted simply generated trees (with S. Janson)
  Combinatorics, Probability and Computing, 31, 368-410, 2022.
• Convergence of trees with a given degree sequence and of their associated laminations (with C. Holmgren and P. Thévenin)
  Submitted, available at arXiv:2111.07748, 2021.
• Trait-dependent branching particle systems with competition and multiple offspring (with A. Sturm and A. Winter)
  Electronic Journal of Probability, 26, 1-41, 2021.
• The k-cut model in deterministic and random trees (with X. S. Cai and C. Holmgren)
  The Electronic Journal of Combinatorics, 28, 1-30, 2021.
• Branching processes with pairwise interactions (with J.C. Pardo)
  Submitted, available at arXiv:2009.11820, 2020. 
• The existence of a giant cluster for percolation on large Crump-Mode-Jagers trees
  Advances in Applied Probability, 52, 266-290, 2020.
• On scaling limits of multitype Galton-Watson trees with possibly infinite variance
  Latin American Journal of Probability and Mathematical Statistics (ALEA), 15, 21-48, 2018.
• The cut-tree of large trees with small heights
  Random Structures & Algorithms, 51, No. 03, 404-427, 2017.
• Asymptotic behaviour near extinction of continuous state branching processes (with J.C. Pardo)
  Journal of Applied Probability, 53, No. 02, 381-391, 2016.
• Yule processes with rare mutation and their applications to percolation on b-ary trees
  Electronic Journal of Probability, 20, No. 43, 1-23, 2015.