Ricardo           CARRIZO VERGARA

About me

I am researcher interested in theoretical and applied aspects of Probability Theory, Mathematical Statistics and Functional Analysis, particularly in the use of generalized stochastic processes and random measures on space-time statistics.

I am currently working on a post-doctorate project in mathematical statistics at the MAP5  Laboratory of the Université Paris-Cité. I work with Angelina ROCHE, Vincent RIVOIRARD, Franck PICARD and Perrine LACROIX in principal component analysis methods for multivariate and marked point processes, which are based on previous works by my collaborators and me.

Previous experiences

Between 2023 and 2025 I worked on a post-doctoral project in Statistical Ecology at the Swiss Ornithological Institute (Schweizerische Vogelwarte), where together with Marc KÉRY and Trevor HEFLEY we worked on models for abundance data  based on an underlying movement of individuals. The Evolving Categories Multinomial distribution, a new multivariate integer-valued distribution, was developed during this post-doc, together with methods of data-fitting and inference of parameters of the underlying movement.

Previously, I spent two years as Research and Teaching Assistant (ATER) in French public institutions, one year at the École Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise (ENS IIE) in Évry, France, and another year at the Université de Paris II: Panthéon-Assas in Paris. In these institutions I collaborated in the teaching of Mathematics and Statistics and I permormed mathematical research on generalized stochastic processes, Karhunen-Loève expansions of random measures, and the possibility of defining stochastic integrals through the analysis of cross-covariance function-measure kernels.

I obtained my PhD in December 2018 at the Geostatistics Team of l'École des Mines de Paris, part of Université Paris Sciences et Lettres (PSL), in Fontainebleau, France. Under the supervision of Nicolas DESASSIS, Denis ALLARD and Hans WACKERNAGEL (R.I.P.), I studied the connection between geostatistical models defined through covariance functions and the solutions of Stochastic Partial Differential Equations (SPDE) in a space-time context (SPDE Approach to Geostatistics). My thesis consists in a treaty exposing the details of the theory, the study of stationary solutions to wide classes of SPDEs (see also our paper on the subject), the cases of some space-time and physically grounded models, and simulation methods based on Fourier Analysis.

While my formal educational background is on engineering and applied mathematics, both from l'École des Mines de Paris and the Pontificia Universidad Católica de Chile,  I have a theoretician approach to my research, with a huge focus on the deep mathematical theory and the philosophy behind the practical methodologies applied by the people I have been working with.

Research interests

• Random Measures, Point processes

• Generalized Stochastic Processes

• Geostatistics (Spatial and Space-time statistics, SPDE Approach)

• Stochastic Analysis (Stochastic Integration, linear SPDEs)

• Population Dynamics, Movement Ecology