My research lies at the interface of probability theory and statistical physics, and has so far focused on the theory of bootstrap percolation, a monotone version of the Glauber dynamics of the Ising model of ferromagnetism, and its application to dynamical models. I recently started research on functional analysis as well.
I am also interested in spectral graph theory and learning.
Publications and preprints
Anisotropic bootstrap percolation in three dimensions. Annals of Probability. Volume 48, Number 5 (2020), 2591-2614. arXiv
Fixation for two-dimensional U-Ising and U-voter dynamics. Journal of Statistical Physics. Volume 182, Number 21 (2021). arXiv
The d-dimensional bootstrap percolation models with axial neighbourhoods. Submitted. arXiv
Three-dimensional 2-critical bootstrap percolation. Submitted. arXiv
Two-dimensional supercritical growth dynamics with one-dimensional nucleation. (joint w. J. Gravner, D. Sivakoff, and L. Wilson). Submitted. arXiv.
Numerical radius in b-Hilbert spaces over 2-inner product spaces. (joint w. O. Ferrer and J. Tovar). Submitted. [pdf].
Ongoing Projects
On heterogeneous bootstrap percolation (joint w. J. Gravner). Available upon request...
On subcritical two-dimensional models (joint w. A. Roldán). In preparation...
Droplet erosion time for U-voter models. In preparation...
Cellular automata with drift in 3D (joint w. P. Barrios and O. Menezes). In preparation...
On a stochastic KDV equation (joint w. A. Mendez). In preparation...
Service at UC Davis.
I organized MP&P seminars for Winter and Spring 2022:
SPRING SEMINARS:
Mar 30: Many Nodal Domains in Random Regular Graphs. by Nikhil Srivastava
Apr 6: Peierls bounds from Toom contours. by Réka Szabó
Apr 13: Chern's conjecture on the Euler Characteristic of affine manifolds. by Camilo Arias
Apr 20: Percolation on Randomly Stretched Lattices. by Augusto Teixeira
Apr 27: Stochastic Billiards with Markovian reflection in generalized parabolic domains. by Conrado Da-Costa
May 11: The contact process over a switching random d-regular graph. by Roberto I. Oliveira
May 25: A coupling approach to quantify the Wasserstein path-distance between Brownian motion and the Goldstein-Kac telegraph process . by Gerardo Barrera
May 31st. Universality for Monotone Cellular Automata. by Rob Morris (In person)
WINTER SEMINARS:
Jan 5th: Some progress on 3D Yang-Mills, by Sourav Chatterjee (Zoom)
Jan 12th: Random walk and Gaussian elimination, by Persi Diaconis (Zoom)
Jan 19th: Sandpile cascades on oscillator networks, by Guram Mikaberidze (Zoom)
Jan 26th: Random Tessellations and Gibbsian Solutions of Hamilton-Jacobi Equations, by Fraydoun Rezakhanlou (Zoom)
Feb 2nd: Spectral asymptotics for contracted tensor ensembles, by Benson Au (Zoom)
Feb 9th: The range of a self-similar additive gamma process is a scale invariant Poisson point process, by Zhiyi You (Zoom)
Feb 16th: The skew Brownian permuton: a new universal limit for random constrained permutations and its connections with Liouville quantum gravity. by Jacopo Borga
Feb 23rd: Stability and chaos in dynamical last passage percolation. by Alan Hammond
Mar 2nd: Occupation time of one-dimensional exclusion processes out of equilibrium. by Tiecheng Xu (Zoom)
Mar 9th: One-sided versus two-sided regularity properties. by A.C.D. van Enter (Zoom, unusual day) (Zoom)
Talks and Events
Bootstrap Percolation with drift. Georgia Tech. Stochastics Seminar. Mar 10, 2022.
An isotropic model in 3 dimensions. SSP2022. Mar 15-19, 2022.
Probabilistic Combinatorics. Universidad de Antioquia. Jun 13-16, 2023.
Automatas celulares monotonos en ambientes aleatorios. Universidad de Cordoba. Jun 23, 2023.