Bienvenidos!
My name is Mario Ayala. I am currently a postdoctoral researcher at the Department of Mathematics at the Technical University of Munich (TU München).
My research sits at the intersection of probability theory and mathematical physics. I am fascinated by the emergence of macroscopic laws from simple microscopic rules of interaction — the so-called micro-to-macro transition. Lately I have also been exploring connections between stochastic analysis and score-based generative models.
My Erdős number is 4:
Me —> Frank Redig —> Pablo A. Ferrari —> Peter E. Ney —> Paul Erdős
Contact: mario.ayala.valenzuela "at" gmail.com
Research lines
Fluctuation fields
Higher-order fluctuations for SEP, SIP, and IRW. Convergence via inductive triangular drift decompositions and L² vanishing estimates.
Applications of duality
Orthogonal duality polynomials (Krawtchouk, Meixner), empirical measure duality, and dressed fields absorbing the carré-du-champ anomaly.
Noise interpretation in SDEs
Itô, Stratonovich, and Klimontovich conventions. Reversibility under coarse-graining and stochastic integral choices in multiplicative noise.