I am an Associate Professor Level A and the Chair of the Department of Probability and Statistics, at IIMAS, UNAM.

From 2017 to 2018, I was a Postdoctoral Newton International Fellow in Pro-L@B at the University of Bath, working with Andreas Kyprianou.

From 2012 to 2016, I was a PhD student at CIMAT, under the supervision of Juan Carlos Pardo and Andreas Kyprianou.

My research interests are in probability theory. Specifically, I am interested in branching process in random environment, multi-type branching processes, self-similar Markov processes, Lévy processes, mathematical biology and coalescent processes.

My Curriculum Vitae.

Preprints

1. The largest fragment in self-similar fragmentation processes of positive index. (with Piotr Dyszewski, Samuel G. G. Johnston and Joscha Prochno).
   ArXiv: 2409.11795 (2024).
2. Absorption and stationary times for the Λ-Wright-Fisher process. (with A. Blancas, A. González-Casanova and S. Hummel).
   ArXiv: 2308.09218 (2023).
3. On multitype Branching Processes with Logistic Competition. (with M.C. Fittipaldi).
   ArXiv: 2203.09701 (2022).

Publications

1. The coalescent structure of Galton-Watson trees in varying environments. (with S. Harris and J. C. Pardo).
   To appear at Annals of Applied Probability. ArXiv: 2207.10923 (2022).
2. Coalescent point process of branching trees in a varying environment. (with A. Blancas).
   Electron. Commun. Probab. 29, 1-15, 2024.
3. Distributional properties of jumps of multi-type CBI processes. (with M. Barczy).
   Electron. J. Probab. 29, 1-39, 2024. ArXiv.
4. Rates on Yaglom’s limit for Galton-Watson processes in varying environment. (with A. Jaramillo and N. Cardona Tobón).
   ALEA, Lat. Am. J. Probab. Math. Stat. 21, 1–23, 2024. ArXiv.
5. Segregational instability of multicopy plasmids: A population genetics approach. (with V. Miro Pina, JCR Hernández-Beltran, A. Siri-Jégousse, R. Peña-Miller and A. González Casanova).
   Ecology and Evolution, volume 12, e9469, (2022).
6. Oscillatory attraction and repulsion from a subset of the unit sphere or hyperplane for isotropic stable Lévy processes. (with M. Kwásniki, A. Kyprianou and T. Saizmaa ).
   In: Chaumont L., Kyprianou A.E. (eds). A Lifetime of Excursions Through Random Walks and Lévy Processes. Progress in Probability, 2021, vol 78. Birkhäuser, Cham. ArXiv.
7. Asymptotic behavior of projections of supercritical multi-type continuous state and continuous time branching processes with immigration. (with M. Barczy and G. Pap).
   Advances in Applied Probability, 2021, 53(4), pp 1023-1060. ArXiv.
8. Yaglom's limit for critical Galton-Watson processes in varying environment: A probabilistic approach. (with N. Cardona-Tobón).
   Bernoulli, 2021, 27(3), pp 1643–1665. ArXiv.
9. Attraction to and repulsion from a subset of the unit sphere for isotropic stable Lévy processes. (with A. Kyprianou and T. Saizmaa ).
   Stochastic Processes and their Applications, 2021, 137, pp 272–293. ArXiv.
10. Backbone decomposition of multitype superprocesses. (with D. Fekete, J.C. Pardo, and J.L. Pérez).
    Journal of Theoretical Probability, 2021, 34, pp 1149–1178. ArXiv.
11. A Note on Characterizing Tightness of Random Sets of Càdlàg Paths. (with N. Freeman).
    Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore. Genealogies of Interacting Particle Systems, pp. 295-313, 2020.
12. Almost sure, L1- and L2-growth behavior of supercritical multi-type continuous state and continuous time branching processes with immigration. (with M. Barczy and G. Pap).
    Sci. China Math. October 2020, Vol. 63(10), pp 2089-2116. ArXiv.
13. Law of large numbers for supercritical superprocesses with non-local branching. (with T. Yang).
    Stochastic Processes and their Applications, Volume 130, Issue 2, February 2020, pp 1074-1102. ArXiv.
14. Almost sure growth of supercritical multi-type continuous-state branching process (with A. Kyprianou and Y.-X. Ren).
    ALEA, Lat. Am. J. Probab. Math. Stat., 2018, 15, pp 409–428. ArXiv.
15. Extinction properties of multi-type continuous-state branching processes (with A. Kyprianou).
    Stochastic Processes and their Applications, Volume 128, Issue 10, October 2018, pp 3466-3489. ArXiv.
16. Asymptotic behaviour of exponential functionals of Lévy processes with applications to random processes in random environment. (with J.C. Pardo and C. Smadi).
    ALEA Lat. Am. J. of Probab. Math. Stat., 2016, 13, pp 1235-1258. ArXiv.
17. Branching processes in a Lévy random environment. (with J.C. Pardo).
    Acta Applicandae Mathematicae, February 2018, Volume 153, Issue 1, pp 55–79. ArXiv.
18. Continuous state branching processes in random environment: The Brownian case. (with J.C. Pardo).
    Stochastic Processes and their Applications, Volume 127, Issue 3, March 2017, pp 957-994. ArXiv.

Theses

• Generalisations of Continuous State Branching Processes. (2016)
  PHD thesis at CIMAT, under the supervision of Juan Carlos Pardo and Andreas Kyprianou.
• Panorama general de la Integral de Henstock. (2012)
  Tesina de Maestría at Facultad de ciencias, UNAM, under the supervision of Guillermo Grabinsky Steider.
• Medida en grupos topológicos. (2010)
  Tesis de Licenciatura at Facultad de ciencias, UNAM, under the supervision of Guillermo Grabinsky Steider.

Ph.D. Students

• Tsogzolmaa Saizmaa (2021, University of Bath)
  Thesis: Conditioned Stable Lévy Processes. Joint supervision with Andreas Kyprianou.
• Natalia Cardona Tobón (2022, CIMAT)
  Thesis: Contributions to branching structures in random environments. Joint supervision with Marcel Ortgiese and Juan Carlos Pardo.

Bachelor Students

• Iván Irving Rosas Domínguez (2023, UNAM)
  Thesis in Spanish: Una aplicación de los procesos estocásticos a un problema de fisiología celular.
• Enrique Moctezuma González (2022, UNAM)
  Thesis in Spanish: Simulación de procesos coalescentes.

Seminario de Probabilidad y Procesos Estocásticos de la UNAM

Este es un seminario entre la Facultad de Ciencias de la UNAM, el Instituto de Matemáticas y el IIMAS. Tiene una frecuencia quincenal en miércoles a las 17hrs.

Para más información visiten la página del seminario Seminario de Probabilidad y Procesos Estocásticos de la UNAM.

El Seminario de Probabilidad Hispanohablante se llevó a cabo todos los lunes a las 19:15 UTC (13:15 hrs México) por zoom.

Seminario de Probabilidad para estudiantes de Posgrado

El seminario esta enfocado para estudiantes de últimos semestre de maestría que quieren hacer una tesis o incluso un doctorado en probabilidad y estadística y están buscando diferentes opciones. La idea del seminario es que sean charlas accesibles cuyo principal propósito es que los estudiantes conozcan diversas áreas activas de investigación en Probabilidad.

De Septiembre de 2021 a Diciembre de 2022, el seminario se llevó a cabo cada quince días, donde un investigador o investigadora presentó una platica de 50 minutos de algún trabajo de una manera accesible. Pueden ver los videos de los participantes en la página del Seminario de Probabilidad para estudiantes de Posgrado.

Talks

Pláticas en español