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, more precisely, on operator theory over 2-inner product spaces.
I am also interested in spectral/quantum graph theory.
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
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). Accepted in Annals of Applied Probability. arXiv.
Positive operators on 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). In preparation...