Publications

You can also find all my publications in my ArXiv webpage: arxiv.org/a/silva_g_2

All the papers below have direct links to their published versions in the journal's webpage and to their arXiv versions. In addition, the published papers are made available with open access, thanks to my current institution USP, after a short period of legal embargo.

Publications

• The Pólya-Tchebotarev problem with semiclassical external fields. Jointly with Victor Alves. 2024, 41 pages. (ArXiv:2403.00719)

• A Central Limit Theorem for intransitive dice. Paper developed under REU-like program, jointly with Luis G. Coelho, Tertuliano Franco, Lael V. Lima, João P. C. de Paula, João V. A. Pimenta and Daniel Ungaretti. 2023, 37 pages. (arXiv:2310.17083)

• Differential equations for the KPZ and periodic KPZ fixed points. Jointly with Jinho Baik and Andrei Prokhorov. Comm. Math. Phys. 401 (2023), 1753-1806.  (journal version, arXiv version) 

• Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation. Jointly with Promit Ghosal.  Comm. Math. Phys. 397 (2023), 1237-1307. (journal version arXiv version)

• Limiting distribution of periodic TASEP. Jointly with Jinho Baik and Zhipeng Liu. Ann. Inst. H. Poincaré Probab. Statist 58 (2022), no. 1, 248–302. (journal version, arXiv version)

• Spectral curves, variational problems and the hermitian matrix model with external source. Jointly with Andrei Martínez-Finkelshtein. Comm. Math. Phys. 383 (2021), 2163-2242. (journal version, arxiv version, final version with open access)

• Large n limit for the product of two coupled random matrices. Jointly with Lun Zhang. Comm. Math. Phys. 377 (2020), no. 3,  2345-2427. (journal version, arxiv version, final version with open access)

• Supercritical regime for the Kissing polynomials. Jointly with Andrew Celsus. J. Approx. Theory 255 (2020). 105408,  42 pages. (journal version and its corrigendum, updated arxiv version, final version with open access)

• The mother body phase transition in the normal matrix model. Jointly with Pavel Bleher. Memoirs of the AMS 265 (2020),  no. 1289.   vi+144 pages. (journal version, arxiv version, final version with open access)

• Critical measures for vector energy: asymptotics of non-diagonal multiple orthogonal polynomials for a cubic weight. Jointly with Andrei Martínez-Finkelshtein. Adv. Math. 349 (2019), 246--315. (published version, arxiv version).

• Critical measures for vector energy: global structure of trajectories of quadratic differentials. Jointly with Andrei Martínez-Finkelshtein. Adv. Math. 302 (2016). 1137--1232. (published version, arxiv version)

•  S-curves in polynomial external fields. Jointly with Arno Kuijlaars. J. Approx. Theory 191 (2015), 1--37. (published version, arxiv version) 

• Critical measures and quadratic differentials in random matrix theory. Ph.D. thesis. KU Leuven, April 2016. xiii+353.  (final version)

Lecture notes

In April-July 2021, I taught a graduate level course on asymptotic methods for special functions and integrable systems in the Graduate Program at the ICMC-USP, Brazil. 

The lecture notes are available here. Sometimes Dropbox complains about permissions to download it, if that happens feel very welcome to contact me for the pdf copy.

Comments are never expected but always appreciated. Use the notes with a grain of salt, as there certainly are typos/imprecisions.

Coauthors

Victor Alves, Jinho Baik, Pavel Bleher, Andrew Celsus, Tertuliano Franco, Promit Ghosal, Arno Kuijlaars, Zhipeng Liu, Andrei Martínez-Finkelshtein, Andrei Prokhorov, Daniel Ungaretti, Lun Zhang.