Personal webpage Gabriel Hernán Berzunza Ojeda

About me

• In 2016, I obtained my PhD at the Institut für Mathematik of the Universität Zürich 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, funded 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. This position was funded by the research grant from the Swedish Foundations Starting Grant from Ragnar Söderbergs Foundation, for the project "Analysis of random graphs and trees with focus on fringe trees, percolation and random networks".

Research interest

Publications

1. Branching processes with pairwise interactions (with Juan Carlos Pardo).
   Latin American Journal of Probability and Mathematical Statistics (ALEA), Vol. 22, 711-748, 2025. arXiv:2009.11820
2. Fringe trees for random trees with given vertex degrees (with Cecilia Holmgren and Svante Janson).
   Random Structures & Algorithms, Vol. 66, 2025. arXiv:2312.04243
3. Invariance principle for fragmentation processes derived from conditioned stable Galton-Watson trees (with Cecilia Holmgren).
   Bernoulli, Vol. 29, 2745-2770, 2023.
   (and error in the proof of Theorem 1 has been corrected to address a gap in the tightness argument, see arXiv:2010.07880)
4. The fluctuations of the giant cluster for percolation on random split trees (with Xing Shi Cai and Cecilia Holmgren).
   Latin American Journal of Probability and Mathematical Statistics (ALEA), Vol. 19, 665–700, 2022. arXiv:1902.08109
5. The asymptotic distribution of cluster sizes for supercritical percolation on random split trees (with Cecilia Holmgren).
   Random Structures & Algorithms, Vol. 60, 631-652, 2022. arXiv:2003.12018
6. The distance profile of rooted and unrooted simply generated trees (with Svante Janson).
   Combinatorics, Probability and Computing, Vol. 31, 368-410, 2022. arXiv:2009.00572
7. Trait-dependent branching particle systems with competition and multiple offspring (with Anja Sturm and Anita Winter).
   Electronic Journal of Probability, Vol. 26, 1-41, 2021. arXiv:1808.09345
8. The k-cut model in deterministic and random trees (with Xing Shi Cai and Cecilia Holmgren).
   The Electronic Journal of Combinatorics, Vol. 28, 1-30, 2021. arXiv:1907.02770
9. The existence of a giant cluster for percolation on large Crump-Mode-Jagers trees.
   Advances in Applied Probability, Vol. 52, 266-290, 2020. arXiv:1806.10686
10. On scaling limits of multitype Galton-Watson trees with possibly infinite variance.
    Latin American Journal of Probability and Mathematical Statistics (ALEA), Vol. 15, 21-48, 2018. arXiv:1605.04810
11. The cut-tree of large trees with small heights.
    Random Structures & Algorithms, Vol. 51, 404-427, 2017. arXiv:1509.01141
12. Asymptotic behaviour near extinction of continuous-state branching processes (with Juan Carlos Pardo).
    Journal of Applied Probability, Vol. 53, 381-391, 2016. arXiv:1308.0549
13. Yule processes with rare mutation and their applications to percolation on b-ary trees.
    Electronic Journal of Probability, Vol. 20, 1-23, 2015. arXiv:1409.3051

Preprints

• Central limit theorem for supercritical Crump-Mode-Jagers processes counted with non-individual random characteristics (with Harlan Connor).
  Submitted, available at arXiv:2511.19391, 2025.
• A tightness criterion for fragmentations (with Cecilia Holmgren and Svante Janson).
  Submitted, available at arXiv:2507.05102, 2025.
• Scaling limit of the Aldous-Broder chain on regular graphs: the transient regime (with Osvaldo Angtuncio Hernandez and Anita Winter).
  Submitted, available at arXiv:2502.06680, 2025.
• On the speed of coming down from infinity for subcritical branching processes with pairwise interactions (with Juan Carlos Pardo).
  Submitted, available at arXiv:2501.06684, 2025.
• Convergence of the pruning processes of stable Galton-Watson trees (with Anita Winter).
  To appear in Bernoulli, 2025+. arXiv:2304.10489
• Convergence of trees with a given degree sequence and of their associated laminations (with Cecilia Holmgren and Paul Thévenin).
  To appear in Stochastic Processes and their Applications, 2025+. arXiv:22111.07748

Extended abstracts

• Fringe trees for random trees with given vertex degrees (with Cecilia Holmgren and Svante Janson).
  35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024), Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Vol. 302, 2024.
• Fragmentation processes derived from conditioned stable Galton-Watson trees (with Cecilia Holmgren).
  33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022), Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Vol. 225, 2022.
• The k-cut model in conditioned Galton-Watson trees (with Xing Shi Cai and Cecilia Holmgren).
  31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020), Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Vo. 159, 2020.
• Largest clusters for supercritical percolation on split trees (with Cecilia Holmgren).
  31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020), Leibniz International Proceedings in Informatics (LIPIcs), Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Vo. 159, 2020.