My research interests lie at the intersection of Markov processes and statistical mechanics. In specific, in the context of interacting particle systems (IPS), my research deals with the application of a type of duality technique to the theory of fluctuations from the hydrodynamic limit.
It is in this direction of research, and for IPS that enjoy the property of self-duality, that the following contributions have materialized:
-  Mario Ayala, Gioia Carinci, and Frank Redig. Quantitative boltzmann–gibbs principles via orthogonal polynomial duality. Journal of statistical physics, 171(6):980–999, 2018.
-  Mario Ayala, Gioia Carinci, and Frank Redig. Condensation of SIP particles and sticky Brownian motion. Submitted to Journal of statistical physics Mario Ayala, Gioia Carinci, and Frank Redig. Higher Order Fluctuation Fields and Orthogonal Duality Polynomials. Submitted to Electronic Journal of Probability
-  Mario Ayala. Hydrodynamic Limit for the Symmetric Inclusion Process. Master Thesis at Tu Delft Mario Ayala,, Casandra Leann Pawling, Adrian Nicholas Smith, Linda Gao, David Hiebeler, and Benjamin Richard Morin. An Epidemiological Approach to the Dynamics of Chytridiomycosis on a Harlequin Frog Population. MTBI 2006 - mtbi.asu.edu