Publications

Publications

Here is a complete list of the 23 published papers.

• 2025

1. Gradual convergence for Langevin dynamics on a degenerate potential.
   Joint work with Milton Jara, IMPA, Brazil and Conrado da Costa, Durham University, UK.
   Stochastic Processes and their Applications 2025.

2. The stability of the multivariate geometric Brownian motion as a bilinear matrix inequality problem.
   Joint work with Eyleifur Bjarkason and Sigurdur Hafstein, University of Iceland, Iceland.
   SIAM (SIADS) Journal on Applied Dynamical Systems 2025.

3. Profile cut-off phenomenon for the ergodic Feller root process.
   Joint work with Liliana Esquivel, University of Puerto Rico, Puerto Rico.
   Stochastic Processes and their Applications 2025.

• 2024

4. Cutoff ergodicity bounds in Wasserstein distance for a viscous energy shell model with Lévy noise.
   Joint work with Juan Carlos Pardo, CIMAT, Mexico, Michael Högele, University of Los Andes, Colombia and Ilya Pavlyukevich,  Jena University, Germany.
   Journal of Statistical Physics 2024.

5. Egerváry's theorems for harmonic trinomials.
   Joint work with Waldemar Barrera and Juan Pablo Navarrete, Autonomous University of Yucatan, Mexico.
   Acta Mathematica Hungarica, 2024.

• 2023

6. The stability region for Schur stable trinomials with general complex coefficients.
   Joint work with Waldemar Barrera and Juan Pablo Navarrete, Autonomous University of Yucatan, Mexico.
   Journal of Dynamics and Differential Equations 2023.

7. Ergodicity bounds for stable Ornstein-Uhlenbeck systems in Wasserstein distance with applications to cutoff stability.
   Joint work with Michael Högele, University of Los Andes, Colombia.
   Chaos: An Interdisciplinary Journal of Nonlinear Science, 2023, Volume 33, Number 11, 113124.

8. Quantitative control of Wasserstein distance between Brownian motion and  the Goldstein-Kac telegraph process.
   Joint work with Jani Lukkarinen, University of Helsinki, Finland.
   Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2023, Volume 59, Number 2, 933-982.
   
   

• 2022

9. The asymptotic distribution of the condition number for random circulant matrices.
   Joint work with Paulo Manrique, National Polytechnic Institute, Mexico.
   Extremes, 2022.

10. Limit behavior of the invariant measure for Langevin dynamics.
    Probability and Mathematical Statistics 2022.

11. Salem-Zygmund inequality for locally sub-Gaussian random variables, random trigonometric polynomials, and random circulant matrices.  
    Boletín de la Sociedad Matemática Mexicana 2022, Volume 28, Number 45.
    Joint work with Paulo Manrique, National Polytechnic Institute, Mexico.

12. The cutoff phenomenon for the stochastic heat and wave equation subject to small Lévy noise.
    Stochastics and Partial Differential Equations: Analysis and Computations 2022.
    Joint work with Juan Carlos Pardo, CIMAT, Mexico and Michael Högele, University of Los Andes, Colombia.

13. On the number of roots for harmonic trinomials.
    Journal of Mathematical Analysis and Applications 2022, Volume 514, Number 2, 126313.
    Joint work with Waldemar Barrera and Juan Pablo Navarrete, Autonomous University of Yucatan, Mexico. Corrigendum.

14. The cutoff phenomenon in Wasserstein distance for nonlinear stable Langevin systems with small Lévy noise.
    Journal of Dynamics and Differential Equations 2022, 1-28.
    Joint work with Juan Carlos Pardo, CIMAT, Mexico and Michael Högele, University of Los Andes, Colombia.
    
    

• 2021

15. The cutoff phenomenon in total variation for nonlinear Langevin systems with small layered stable noise.
    Electronic Journal of Probability 2021, Volume 26, Number 119, 2021, 1-76.
    Joint work with Juan Carlos Pardo, CIMAT, Mexico and Michael Högele, University of Los Andes, Colombia.

16. Cutoff thermalization for Ornstein-Uhlenbeck systems with small Lévy noise in the Wasserstein distance.
    Journal of Statistical Physics 2021, Volume 184, Number 27, 1-54.
    Joint work with Juan Carlos Pardo, CIMAT, Mexico and Michael Högele, University of Los Andes, Colombia.

17. Zero-free neighborhood around the unit circle for Kac polynomials.
    Periodica Mathematica Hungarica 2021, 84, 159-176.
    Joint work with Paulo Manrique, National Polytechnic Institute, Mexico. 

18. Cutoff phenomenon for the maximum of a sampling of Ornstein-Uhlenbeck processes.
    Statistics and Probability Letters 2021, Volume 168, 108954. 

19. A switch convergence for a small perturbation of a linear recurrence equation.
    Brazilian Journal of Probability and Statistics 2021, Volume 35, Number 2, 224-241.
    Joint work with Shuo Liu, University of Alberta, Canada.
    
    

• 2020

20. Cut-off phenomenon for the Ornstein-Uhlenbeck processes driven by Lévy processes.
    Electronic Journal of Probability 2020, Volume 25, Number 15, 1-33.
    Joint work with Juan Carlos Pardo, CIMAT, Mexico.

21. Thermalisation for small random perturbations of dynamical systems.
    Annals of Applied Probability 2020, Volume 30, Number 3, 1164-1208.
    Joint work with Milton Jara, IMPA, Brazil.
    
    

• 2018

22. Abrupt convergence for a family of Ornstein-Uhlenbeck processes.
    Brazilian Journal of Probability and Statistics 2018, Volume 32, Number 1, 188-199.
    
    

• 2016

23. Abrupt convergence for stochastic small perturbations of one dimensional dynamical systems.
    Journal of Statistical Physics 2016, Volume 163, Number 1, 113-138.
    Joint work with Milton Jara, IMPA, Brazil.

Preprints

Here is a list of projects that are submitted for publication.

• 2025

1. Wasserstein error estimates between telegraph processes and Brownian motion.
   Joint work with Jani Lukkarinen, University of Helsinki, Finland, and Mikko S. Pakkanen, Imperial College London, UK.
   Submitted.

2. Ergodicity bounds in the sliced Wasserstein distance for Schur stable autoregressive processes.
   Joint work with Michael Högele, University of Los Andes, Colombia, Paulo Henrique da Costa, University of Brasilia, Brazil.
   Submitted.

3. Cut-off phenomenon and asymptotic mixing for multivariate general linear processes.
   Joint work with Michael Högele, University of Los Andes, Colombia, Pauliina Ilmonen and Lauri Viitasaari, Aalto University, Finland.
   Submitted.

4. Cutoff stability of multivariate geometric Brownian motion.
   Joint work with Juan Carlos Pardo, CIMAT, Mexico and Michael Högele, University of Los Andes, Colombia.
   Submitted.

• 2024

5. Ergodicity for locally monotone stochastic evolution equations with Lévy noise.
   Joint work with Jonas Tölle, Aalto University, Finland.
   Submitted.

Work in Progress

Here is a list of projects that are in preparation and should become papers soon.

• Limit theorems for coagulations equations: simple kernels. Joint work with Marina Amado Ferreira, Toulouse Mathematics Institute , University of Toulouse  and Alessia Nota, Gran Sasso Science Institute (GSSI).

• Cut-off phenomenon for expanding maps on the circle. 

Outreach

Here is a list of divulgation papers.

1. Notas sobre algunos teoremas de Jenö Egerváry.
   Joint work with Waldemar Barrera, Miguel Angel Can Ek and Juan Pablo Navarrete, Autonomous University of Yucatan, Mexico.
   Abstraction And Application, 2022, Volume 38, Number 4, 50-59.

Coauthors

Here is a list of coauthors in alphabetic order (I have already published at least one paper with them).

• Conrado da Costa, University of São Paulo, Brazil.

• Eyleifur Bjarkason, University of Iceland, Iceland.

• Ilya Pavlyukevich,  Jena University, Germany.

• Jani Lukkarinen, University of Helsinki, Finland.

• Jonas Tölle, Aalto University, Finland.

• Juan Carlos Pardo, Center for Research in Mathematics, CIMAT, Mexico.

• Juan Pablo Navarrete, Autonomous University of Yucatan, Mexico.

• Lauri Viitasaari,  Aalto University, Finland.

• Liliana Esquivel, University of Puerto Rico, Puerto Rico.

• Milton Jara, Instituto Nacional de Matemática Pura e Aplicada, IMPA, Brazil.

• Michael Högele, Universidad de Los Andes, Colombia.

• Mikko S. Pakkanen, Imperial College London, U.K.

• Shuo Liu, University of Alberta, Canada.

• Sigurdur Hafstein, University of Iceland, Iceland.

• Paulo Henrique da Costa, University of Brasilia, Brazil.

• Pauliina Ilmomen,  Aalto University, Finland.

• Paulo Manrique,  National Polytechnic Institute, Mexico.

• Waldemar Barrera, Autonomous University of Yucatan, Mexico.