Research
In construction...
Main interests:
- Equilibrium Statistical Mechanics: Cluster expansions, Pirogov-Sinai, Phase Transitions, Ground states, Gibbs measures, Ising type models, KMS states.
- Ergodic Theory, Dynamical Systems and Operator Algebras: Thermodynamic Formalism; Equilibrium, Conformal and Gibbs measures; Countable Markov shifts, Ergodic Optimization, Chaos at zero temperature, Symbolic dynamics, Cuntz–Krieger and Exel-Laca algebras.
- Combinatorics: Probabilistic Method, Lovász Local Lemma, Entropy Compression, Generating Functions, Coloring and Counting Problems.
Co-authors:
- Lucas Affonso (3) (University of São Paulo (USP), Brazil)
- Noga Alon (1) (Princeton University, USA/Tel Aviv University, Israel)
- Sebastián Barbieri (1) (Universidad de Santiago de Chile, Chile)
- Elmer R. Beltrán (2) (Universidad Nacional Jorge Basadre Grohmamn, Peru)
- Luísa Borsato (1) (University of São Paulo (USP), Brazil)
- Raimundo Briceño (1) (Pontificia Universidad Católica de Chile (UC), Chile)
- Marzio Cassandro (1) (Gran Sasso Science Institute (GSSI), Italy)
- Leandro Cioletti (2) (University of Brasília, Brazil)
- Luís Doin (1) (University of São Paulo (USP), Brazil)
- Eric O. Endo (7) (NYU Shanghai, China)
- Aernout van Enter (4) (University of Groningen, the Netherlands)
- Ruy Exel (2) (Federal University of Santa Catarina, Brazil)
- Roberto Fernández (2) (NYU Shanghai, China/Utrecht University, the Netherlands)
- Rodrigo Frausino (2) (University of Wollongong (UOW), Australia)
- Ricardo Freire (1) (University of São Paulo (USP), Brazil)
- Eduardo Garibaldi (2) (UNICAMP, Brazil)
- Satoshi Handa (1) (Hokkaido University, Japan)
- Bruno Kimura (2) (Hokkaido University, Japan)
- Marcelo Laca (1) (University of Victoria, Canada)
- Arnaud Le Ny (2) (UMR CNRS 8050, Université Paris-Est, France)
- João Maia (2) (University of São Paulo (USP), Brazil)
- Rafael Pereira (1) (Victoria University of Wellington, New Zealand)
- Errico Presutti (1) (Gran Sasso Science Institute (GSSI), Italy)
- Aldo Procacci (2) (Federal University of Minas Gerais (UFMG), Brazil)
- Thiago Raszeja (3) (AGH University of Science and Tecnology, Poland)
- Wioletta M. Ruszel (2) (Utrecht University, the Netherlands)
- Benedetto Scoppola (1) (University of Rome Tor Vergata, Italy)
- Philippe Thieullen (2) (Université de Bordeaux, France)
- Gregório Dalle Vedove (1) (University of São Paulo (USP), Brazil)
Publications:
13. Quasi-invariant measures for generalized approximately proper equivalence relations. Journal of Mathematical Analysis and Applications, v. 538, Issue 2, p. 128444, (2024) (Journal) (arxiv). (with Ruy Exel, Rodrigo Frausino and Thiago Raszeja).
12. Infinite DLR Measures and Volume-Type Phase Transitions on Countable Markov Shifts. Nonlinearity, v. 34, Number 7, p. 4819-4843, (2021). (Journal) (arxiv). (with Eric O. Endo and Elmer Beltrán) Talk at the Bernoulli-IMS One World Symposium 2020 about the paper (video).
11. Entropic repulsion and lack of the g-measure property for Dyson models. Communications in Mathematical Physics. v. 363, Issue 3, p. 767-788. (2018). (Journal) (arxiv) (with Aernout van Enter, Eric O. Endo and Arnaud Le Ny). Talk by Eric Endo at the XXI Brazilian School of Probability (video).
10. Zero-temperature phase diagram for double-well type potentials in the summable variation class. Ergodic Theory and Dynamical Systems. v. 38, Issue 3, p. 863-885, (2018). (Journal) (arxiv) (with Eduardo Garibaldi and Philippe Thieullen).
9. Contour methods for long-range Ising models: weakening nearest-neighbor interactions and adding decaying fields. Annales Henri Poincaré v. 19, Issue 8, 2557-2574, (2018). (Journal) (arxiv) (with Aernout van Enter, Eric O. Endo, Bruno Kimura and Wioletta M. Ruszel).
8. Stability of the Phase Transition of Critical-Field Ising Model on Cayley trees under Inhomogeneous External Fields. Stochastic Processes and their Applications v. 127, Issue 12, p. 4126-4138, (2017). (Journal) (arxiv) (with Aernout van Enter and Eric O. Endo).
7. Counting Contours on Trees. Letters in Mathematical Physics v. 107 p. 887–899, (2017). (Journal) (arxiv). (with Noga Alon and Eric O. Endo).
6. Phase Transitions in Ferromagnetic Ising Models with spatially dependent magnetic fields. Communications in Mathematical Physics v. 337, Issue 1, p. 41-53, (2015). (Journal) (arxiv) (with Leandro Cioletti, Marzio Cassandro and Errico Presutti).
5. On the existence of maximizing measures for irreducible countable Markov shifts: a dynamical proof. Ergodic Theory and Dynamical Systems. v. 34, Number 4, p. 1103-1115, (2014). (Journal) (arxiv) (with Ricardo Freire) .
4. An Improvement of the Lovász Local Lemma via Cluster Expansion. Combinatorics, Probability and Computing. v. 20, Issue 5, pp. 709-719 (2011). (Journal) (arxiv) (with Roberto Fernández , Aldo Procacci and Benedetto Scoppola).
3. On the Convergence of Cluster Expansions for Polymer Gases. Journal of Statistical Physics, v. 139, Number 4, p. 598-617. (2010) (with Roberto Fernández and Aldo Procacci) (Journal) (arxiv).
2. Weak KAM methods and ergodic optimal problems for countable Markov shifts. Bulletin of the Brazilian Mathematical Society, V. 41, Number 3, p. 321-338.(2010) (with Eduardo Garibaldi) (Journal) (arxiv).
1. Phase Transition in Ferromagnetic Ising Models with Non-uniform External Magnetic Fields. Journal of Statistical Physics, v. 139, Number 5, p. 769-778. (2010). (with Leandro Cioletti) (Journal) (arxiv).
Accepted:
1. Thermodynamic formalism for amenable groups and countable state spaces. (2024) (Journal) (arxiv) (with Elmer Beltrán, Luísa Borsato, and Raimundo Briceño) To appear in the Journal of the Institute of Mathematics of Jussieu.
Surveys, proceedings, and chapters of books
1. Dyson models under renormalization and in weak fields. (Journal) (arxiv). (with Aernout van Enter, Eric O. Endo, Bruno Kimura, Arnaud Le Ny and Wioletta M. Ruszel). Sojourns in Probability Theory and Statistical Physics - I Spin Glasses and Statistical Mechanics, A Festschrift for Charles M. Newman. Vladas Sidoravicius (Ed.) Pages 123-137, (2019).
Preprints
8. Phase Transitions in the semi-infinite Ising model with a decaying field. (Journal) (arxiv) (with João Maia)
7. Gibbs Measures on Multidimensional Spaces. Equivalences and a Groupoid Approach. (Journal) (arxiv) (with Bruno Hideki Fukushima-Kimura, Rafael Pereira Lima, Thiago Raszeja).
6. Phase Transitions in Multidimensional Long-Range Random Field Ising Models. (Journal) (arxiv) (with Lucas Affonso and João Maia)
5. Quantum Statistical Mechanics via Boundary Conditions. A Groupoid Approach to Quantum Spin Systems. (Journal) (arxiv) (with Lucas Affonso and Marcelo Laca)
4. Chaos in Bidimensional Models with Short-Range. (Journal) (arxiv) (with Sebastián Barbieri, Philippe Thieullen, Gregório Dalle Vedove).
3. Long-Range Ising Models: Contours, Phase Transitions and Decaying Fields. (Journal) (arxiv) (with Lucas Affonso, Eric O. Endo, Satoshi Handa).
Lucas Affonso's talk in the Probability Seminar at the Federal University of Rio de Janeiro (UFRJ) about the paper (video).
My talk at the Helsinki Mathematics and Physics Seminar about the paper (video). (slides)
2. Entropy Compression Method and Legitimate Colorings in Projective Planes. (Journal) (arxiv). (with Luís Doin).
1. Thermodynamic Formalism for Generalized Markov Shifts on Infinitely Many States. (Journal) (arxiv). (with Ruy Exel, Rodrigo Frausino and Thiago Raszeja).
Ruy Exel's talk at ICM 2018 about the paper (video). [At this moment, only constant potential, see the lectures below]
My talk at the Universidade Federal do Rio Grande do Sul (UFRGS) about the paper (video)
My talk at the Universidade do Porto about the paper (video). [incomplete results]