Bio
Caio Alves is a mathematician with a focus on discrete probability, particularly in the areas of random graphs and percolation theory. Initially rooted in pure mathematics, his work aims to explore the fundamental aspects of probabilistic systems, such as connectivity and emergent properties in networks.
Recently, Caio has broadened his scope to include applied mathematics. He is presently working on projects related to low-rank approximations in semiring spaces and signal processing filtering techniques. This shift represents his interest in applying mathematical concepts to practical problems.
As part of his ongoing professional development, Caio is also gaining expertise in emerging fields like quantum computing and graph neural networks. He seeks to understand how these technologies can be informed by, and benefit from, established mathematical principles.
Professional Experience
Caio Alves began his postdoctoral research in Probability Theory at the University of Leipzig, where he worked under the supervision of Professor Artëm Sapozhnikov until August 2020. In September of the same year, he relocated to Budapest to join the Alfréd Rényi Institute of Mathematics. There, he continued his postdoctoral research under the supervision of Gábor Pete.
As of November 2022, Caio has taken on the role of Research Scientist at the Mathematics in Computation section of the Oak Ridge National Laboratory.
His academic foundation was laid at the Federal University of Minas Gerais (UFMG), where he completed his undergraduate, Masters, and PhD programs in the Math Department. His doctoral research was conducted under the guidance of Professor Serguei Popov at the Statistics Department of Unicamp.
Other Publications
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).