My research lies at the interface of probability theory and statistical physics, and is mostly 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, more precisely, on operator theory over 2-inner product spaces.
I am also interested in spectral/quantum graph theory and mathematical statistics.
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. Stochastic Processes and their Applications. Volume 174 (2024). arXiv
Two-dimensional supercritical growth dynamics with one-dimensional nucleation. (joint w. J. Gravner, D. Sivakoff, and L. Wilson). Annals of Applied Probability. 35(5): 3378-3411 (October 2025). arXiv.
Three-Dimensional 2-Critical Bootstrap Percolation: The Stable Sets Approach. Random Structures & Algorithms 68, no. 4: e70083. https://doi.org/10.1002/rsa.70083 (July 2026). arXiv
Mean absorption time for the coalescing process with removal. (joint w. M. Estrada). Submitted. Available upon request.
Positive operators on b-Hilbert spaces over 2-inner product spaces. (joint w. O. Ferrer and J. Tovar). Submitted. [pdf].
Sharp upper bounds on the maximum degree of star-free graphs under different planarity conditions. (joint w. J. Saurith). Submitted.
Entropy threshold for some sampling designs. (joint w. C. Arrieta). Submitted.
Ongoing Projects
Symmetric monotone cellular automata. (joint w. L. Aragão). In preparation...
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). In preparation...