Marcelo Durães Capeleiro Pinto (4C1C-38C3-ED55)

Curriculum Vitae

Marcelo Durães Capeleiro Pinto

I obtained a PhD in Math in 2025 at PUC-Rio in the field of dynamical systems and ergodic theory. My research is related to the regularity theory and statistical properties of the Lyapunov exponents from random linear cocycles.

Identification

Personal identification

Full name: Marcelo Durães Capeleiro Pinto

Citation names

Durães, Marcelo

Author identifiers

Ciência ID: 4C1C-38C3-ED55
ORCID iD: 0000-0003-3425-8491

Knowledge fields

Exact Sciences - Mathematics

Languages

Language	Speaking	Reading	Writing	Listening	Peer-review
Portuguese (Mother tongue)
English
Spanish; Castilian
French

Education

	Degree	Classification
2025/09 - 2026 Ongoing	Matemática (Pós-doutoramento) Major in Sistemas Dinâmicos e Teoria Ergódica Universidade de Lisboa Faculdade de Ciências, Portugal
2021 - 2025/04/15 Concluded	Matemática (Doctor) Major in Sistemas Dinâmicos e Teoria Ergódica Pontifícia Universidade Católica do Rio de Janeiro, Brazil " Lyapunov Exponents of Random Linear Cocycles: Regularity and Statistical Properties" (THESIS/DISSERTATION)
2019 - 2021 Concluded	Matemática (Master) Major in Sistemas Dinâmicos e Teoria Ergódica Pontifícia Universidade Católica do Rio de Janeiro, Brazil "Hölder continuity for Lyapunov exponents of random linear cocycles" (THESIS/DISSERTATION)
2014 - 2018 Concluded	Matemática (Bachelor) Pontifícia Universidade Católica do Rio de Janeiro, Brazil

Outputs

Publications

Journal article

Pedro Duarte; Marcelo Durães; Tomé Graxinha; Silvius Klein. "Random 2D linear cocycles II: Statistical properties". Journal of Spectral Theory (2026): https://doi.org/10.4171/jst/601.
10.4171/jst/601

Other

Other output

Analyticity of the Lyapunov exponents of random products of matrices. This paper is concerned with the study of random (Bernoulli and Markovian) product of matrices on a compact space of symbols. We establish the analyticity of the maximal Lyapunov exponent as a function of the transition probabilities, thus extending the results and methods of Y. Peres from a finite to an infinite (but compact) space of symbols.. 2025. Durães, Marcelo; Melo, Aline; Amorim, Artur. https://arxiv.org/abs/2501.19286.
Random 2D linear cocycles I: dichotomic behavior. In this paper we establish a Bochi-Mañé type dichotomy in the space of two dimensional, nonnegative determinant matrix valued, locally constant linear cocycles over a Bernoulli or Markov shift. Moreover, we prove that Lebesgue almost every such cocycle has finite first Lyapunov exponent, which then implies a break in the regularity of the Lyapunov exponent, from analyticity to discontinuity.. 2025. Durães, Marcelo; Klein, Silvius; Duarte, Pedro; Graxinha, Tomé. https://arxiv.org/abs/2503.21050.
Hölder continuity of the Lyapunov exponent for Markov cocycles via Furstenberg's Formula. This paper is concerned with the study of linear cocycles over uniformly ergodic Markov shifts on a compact space of symbols. We establish the joint Hölder continuity of the maximal Lyapunov exponent as a function of the cocycle and the transition kernel in the vicinity of any irreducible cocycle with simple maximal Lyapunov exponent.. 2022. Durães, Marcelo; Melo, Aline; Klein, Silvius; Cai, Ao. https://arxiv.org/abs/2212.00174.