Caio Alves

About me

I am Caio Alves, a Brazilian mathematician.

I was a postdoc researching Probability Theory. Up until August 2020, I was in the University of Leipzig under the supervision of Professor Artëm Sapozhnikov. In September 2020 I moved to Budapest to work at the Alfréd Rényi Institute of Mathematics under the supervision of Gábor Pete.

Since November 2022, I am a Research Scientist at the Mathematics in Computation section of the Oak Ridge National Laboratory

I did my undergrad, my Masters and my PhD at the Math Department of the Federal University of Minas Gerais - UFMG. My PhD was made under the supervision of Professor Serguei Popov at the Statistics department of Unicamp.

My main research interest is in Percolation Theory, specifically in models with long range correlation such as Random Interlacements, Loop percolation, and the Cylinder Percolation model. I am also interested in Random Graph models, such as the Configuration Model and graphs generated by Preferential Attachment Rules.

Contact Information

My email is caiotmalves followed by the common ending of google emails

Preprints and Publications

Large communities in a scale-free network. With Rodrigo Ribeiro and Rémy Sanchis. Journal of Statistical Physics 166.1 (2017): 137-149.

A note on truncated long-range percolation with heavy tails on oriented graphs. with Marcelo R. Hilário, Bernardo NB De Lima, and Daniel Valesin. Journal of Statistical Physics 169.5 (2017): 972-980.

Conditional decoupling of random interlacements. With Serguei Popov. Latin American Journal of Probability and Mathematical Statistics. 15. 10.30757/ALEA.v15-38. (2018)

Preferential Attachment Random Graphs with Edge-Step Functions. With Rodrigo Ribeiro and Rémy Sanchis. arXiv preprint arXiv:1704.08276 (2017). Accepted for publication in the Journal of Theoretical Probability.

Decoupling inequalities and supercritical percolation for the vacant set of random walk loop soup. With Artem Sapozhnikov. . Electron. J. Probab., 24:1–34, (2019).

Clustering in preferential attachment random graphs with edge-steps. With Rodrigo Ribeiro and Rémy Sanchis. arXiv preprint arXiv:1901.02486 (2019). Accepted for publication in Journal of Applied Probability.

Diameter of P.A. random graphs with edge-step functions. With Rodrigo Ribeiro and Rémy Sanchis. arXiv preprint arXiv:1902.10165 (2019). Accepted for publication in Random Structures and Algorithms.

Sharp threshold for two-dimensional majority dynamics percolation. With Rangel Baldasso. Annales de l’Institut Henri Poincaré (2022).

Asymptotic Results of a Multiple-entry Reinforcement Process. With Rodrigo Ribeiro Daniel Valesin. Stochastic Processes and their applications (2023).

Spread of Infection over P.A. random graphs with edge insertion, With Rodrigo Ribeiro. ALEA (2022).

Percolation phase transition on planar spin systems. With Rangel Baldasso, Gideon Amir, and Augusto Teixeira. arXiv preprint arXiv:2105.13314 (2021).

Clustering and Cliques in P.A random graphs with edge insertion. With Rodrigo Ribeiro and Rémy Sanchis. arXiv arXiv:1902.10165 (2021).

Cylinders’ percolation: decoupling and applications. With Augusto Teixeira. arXiv preprint arXiv:2112.10055 (2021).

Teaching

Here is the website of the course IPSP Math 2 taught in the Summer semester of 2018

The site of the percolation course taking place in the Spring 2021 at the Budapest university of Techonology and Economics can be found here (or clicking the link at the beginning of this page).

Friends, mentors and collaborators

Serguei Popov

Augusto Teixeira

Artëm Sapozhnikov

Daniel Valesin

Rodrigo Ribeiro

Bernardo Lima

Marcelo Hilário

Daniel Ungaretti

Remy Sanchis