My name is Arturo Jaramillo Gil. Since September of 2018, I am a postdoctoral researcher in a collateral agreement between the universities of Luxembourg and Singapore. I work in collaboration with the research group of professors Ivan Nourdin, Giovanni Peccati, Adrian Röllin and Louis H.Y. Chen on topics of stochastic analysis and Stein's method. 

Arturo Jaramillo
Photo of Me

In 2006, I studied my Bachelor in science, specialized in mathematics, at the University of Guanajuato (UG). My bachelor thesis advisor was professor Daniel Hernández and my thesis was oriented to the application of differential geometry and stochastic analysis in infinite dimensions, to the study of interest rates and bonds. In 2011, I started studying my master in science, specialized in probability and statistics at the Center of Research in Mathematics (CIMAT). My master thesis advisor was professor Juan Carlos Pardo Millán and my thesis consisted on the study of central and non-central limit theorems for multiple Skorohod integrals. In 2018 I obtained my PhD in mathematics at The University of Kansas (KU). While studying in KU, I conducted research on limit theorems and Malliavin calculus under the supervision of professor David Nualart. During my postdoc in the Université du Luxembourg and the National University of Singapore, I have developed research on Stein's method, local times, Gaussian processes, random matrices and number theory in collaboration with Giovanni Peccati, Ivan Nourdin, Louis Chen and Adrian Röllin.


My main areas of interest are stochastic analysis on Wiener space, limit theorems, fractional Brownian motion, Stein's method, local times, random matrices and probabilistic number theory.  Next you can find a list of my most recent publications:


            A. Jaramillo, D. Nualart
            Collision of eigenvalues for matrix-valued processes 
            Random matrices: Theory and Applications (to appear).

            A. Jaramillo, JC. Pardo, JL Pérez 
            Convergence of the empirical spectral distribution of Gaussian matrix-valued processes.
           Electronic Journal of Probability (2019) 10.

            A. Jaramillo, D. Nualart.
            Functional limit theorem for the self-intersection local time of the fractional Brownian motion.
            Annales de l'institut Henri Poincaré (2019) 22, 481-528.

            D. Harnett, A. Jaramillo, D. Nualart.
            Symmetric stochastic integrals with respect to a class of self-similar Gaussian processes.
            Journal of Theoretical Probability (2019) 3, 1105-1144.

            A. Jaramillo, D. Nualart
            Asymptotic properties of the derivative self-intersection local time of fractional Brownian motion.
            Stochastic Processes and Their Applications (2017) 127, 669-700.

            O. Arizmendi, A. Jaramillo
            Convergence of the fourth moment and Infinite Divisibility: Quantitative Estimates. 
            Electronic Communications in Probability (2014) 19, 1-12.


            M. Diaz, A. Jaramillo, JC. Pardo
            Fluctuations of matrix-valued Gaussian processes Arxiv file.

            A. Jaramillo, I. Nourdin, G. Peccati
            Approximation of local times: zero energy and weak derivatives. Arxiv file.


             PhD Thesis.
             A. Jaramillo. Limit distributions for functionals of Gaussian processes.
            Supervisor David Nualart.

             Master in Science Thesis.
             A. Jaramillo. Central limit theorems for multiple Skorohod integrals.
             Supervisor Juan Carlos Pardo Millán. Written in Spanish.
             Based on previous work elaborated by David Nualart and Ivan Nourdin.

             Bachelor thesis.
             A. Jaramillo. Invariant manifolds and finite dimensional realizations.
             Supervisor Daniel Hernández. Written in Spanish.
             Based on previous work elaborated by Tomas Bjork.



Here is a list of my recent talks

Organization Date Presentation
UNAM May 2020 Teorema de Erdös-Kac para funciones aditivas
Technische universität Berlin March 2020 A self-contained probabilistic approach to Erdös-Kac theorem
National University of Singapore November 2020 Probabilistic Kubilius theorem
National University of Singapore September 2020 A first approach to Gaussian Multiplicative chaos
Université du Luxembourg September 2018 Fluctuations of the spectrum of GOE processes
XIII Simposio de Probabilidad, UNAM. December, 2017 Eigenvalue collision
Ergodic properties of Markov chains course. KU November 21, 2017 Transport Inequalities
Combinatorics seminar, KU. April 14, 2017 Cumulants and moments for products of free random variables
Probability seminar, KU March 15, 2017 Empirical spectral distribution of Gaussian matrix processes
GSO seminar, KU Spring 2017 A geometric view of interest rate theory
Free Probability seminar, CIMAT. January 12, 2017 Divisibilidad infinita libre, teoremas de convergencia
Algebraic combinatorics course, KU. December 14, 2016 Non crossing partitions in free probability
Combinatorics seminar, KU. November 11, 2016 Relations between cumulants in non commutative probability
GSO seminar, KU. Fall 2016 The five natural notions of independence