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research
Research Interests
  • Probability Theory, in special Interacting Particle Systems. My main subjects are Hydrodynamic Limit, Fluctuations, Large Deviations, and its connections with Statistical Mechanics and Partial Differential Equations.
Research Publications
  • D. Erhard, T. Franco, J. de Jesus Santana
    A strong large deviation principle for the empirical measure of random walks, 2024.
    https://arxiv.org/abs/2409.01290

  • D. Erhard, T. Franco, M. Jara and E. Pimenta.
    A Functional Central Limit Theorem for the General Brownian Motion on the Half-Line, 2024.
    http://arxiv.org/abs/2408.06830

  • Luis G. Coelho, Tertuliano Franco, Lael V. Lima, João P. C. de Paula and João V. A. Pimenta, Guilherme L. F. Silva and Daniel Ungaretti.
    A Central Limit Theorem for intransitive dice.
    Submitted to publication, 2023.
    https://arxiv.org/abs/2310.17083

  • T. Franco e D. S. D. da Silva. Teorema de Bayes e o Paradoxo da Ilha (artigo de divulgação científica)
    Revista Hipátia, UFBA, 2023. Disponível on-line em:
    http://www.dmat.ufba.br/extensao/revista-hip%C3%A1tia

  • D. Erhard, T. Franco and T. Xu. Nonequilibrium Joint Fluctuations for Current and Occupation Time in The Symmetric Exclusion Process.
    Electronic Journal of Probability 2024, Vol. 29, paper no. 76, 1-53.
    Link to journal

  • T. Franco, P. Gonçalves, A. Neumann. Large Deviations for the SSEP with slow boundary: the non-critical case.
    ALEA, Lat. Am. J. Probab. Math. Stat. 20, 359--394 , 2023.
    https://doi.org/10.30757/ALEA.v20-13

  • D. Erhard, T. Franco, G. Reis., The Directed Edge Reinforced Random Walk: The Ant Mill Phenomenon.
    Journal of Statistical Physics 190, 18, 2023.
    Link to journal

  • T. Franco, P. Gonçalves, C. Landim, A. Neumann. Dynamical Large Deviations For The Boundary Driven Symmetric Exclusion Process With Robin Boundary Conditions.
    ALEA, Lat. Am. J. Probab. Math. Stat. 19, 1497--1546 , 2022.
    Link to journal

  • T. Franco, L. A. Gurgel, B. N. de Lima. Large deviations in the supremum norm for a reaction–diffusion system.
    Braz. J. Probab. Stat. 36 (1) 45--80, March 2022.
    Link to journal

  • D. Erhard, T. Franco, D. S. da Silva. The slow bond random walk and the snapping out Brownian motion.
    Ann. Appl. Probab. Volume 31, Number 1, pages 99--127, 2021.
    Link to journal
    PDF

  • D. Erhard, T. Franco, P. Gonçalves, A. Neumann and M. Tavares. Non-equilibrium fluctuations for the SSEP with a slow bond.
    Ann. Inst. H. Poincaré Probab. Statist. Volume 56, Number 2, pages 1099--1128, 2020.
    Link to journal

  • T. Franco and M. Tavares. Hydrodynamic Limit for the SSEP with a Slow Membrane.
    Journal of Statistical Physics, Vol. 175, Issue 2, pages 233--268, 2019.
    Link to journal

  • T. Franco, P. Gonçalves, A. Neumann. Non-equilibrium and stationary fluctuations of a slowed boundary symmetric exclusion.
    Stochastic Processes and their Applications, Vol. 129, Issue 4, pages 1413--1442, 2019.
    Link to journal

  • T. Franco, A. Neumann. Large deviations for the exclusion process with a slow bond.
    Annals of Applied Probability Vol. 27, No. 6, 3547--3587, 2017.
    Link to journal

  • T. Franco. Phase transition in the KMP model with slow/fast boundaries.
    Markov Processes and Related Fields, Volume 23, Issue 1, 171--186, 2017.
    http://arxiv.org/abs/1601.04042
    Link to journal

  • T. Franco, P. Gonçalves, M. Simon. Crossover to the stochastic Burgers equation for the WASEP with a slow bond.
    Communications in Mathematical Physics, Volume 346, n.3, 801--838, 2016.
    Link to journal

  • T. Franco, P. Gonçalves, G. M. Schütz. Scaling limits for the exclusion process with a slow site.
    Stochastic Processes and their Applications, Volume 126, Issue 3, Pages 800–831, 2016.
    Link to journal

  • L. Avena, T. Franco, M. Jara, F. Völlering. Symmetric exclusion as a random environment: hydrodynamic limits.
    Ann. Inst. H. Poincaré Probab. Statist. Volume 51, Number 3 (2015), 901-916.
    Link to journal

  • T. Franco, J. Haddad. Continuous dependence on the derivative of generalized heat equations.
    Differential and Integral Equations, Volume 28, Numbers 1-2 (2015), 59–78.
    Link to journal

  • T. Franco, P. Gonçalves, A. Neumann. Phase Transition of a Heat Equation with Robin's Boundary Conditions and Exclusion Process.
    Trans. Amer. Math. Soc. 367 (2015), 6131-6158.
    Link to journal

  • T. Franco, P. Gonçalves, A. Neumann. Occupation time of exclusion processes with conductances.
    Journal of Statistical Physics, Volume 156, Issue 5 (2014), Page 975-997.
    Link to journal

  • T. Franco, P. Gonçalves, A. Neumann. Phase transition in equilibrium fluctuations of symmetric slowed exclusion.
    Stochastic Processes and their Applications, Volume 123, Issue 12, December 2013, Pages 4156-4185.
    Link to journal
    together with: T. Franco, P. Gonçalves, A. Neumann. Corrigendum to: Phase transition in equilibrium fluctuations of symmetric slowed exclusion.
    Stochastic Process and their Applications, Volume 126, Issue 10, October 2016, Pages 3235-3242.
    Link to journal

  • T. Franco, P. Gonçalves, A. Neumann. Hydrodynamical Behavior of Symmetric Exclusion with Slow Bonds.
    Ann. Inst. H. Poincaré Probab. Statist. Volume 49, Number 2 (2013), 402-427.
    Link to journal

  • T. Franco, P. Groisman. A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-up Time.
    Journal of Statistical Physics, Volume 149, Issue 4, pp 629-642, November (2012).
    Link to journal

  • T. Franco, A. Neumann, G. Valle. Hydrodynamic Limit for a Class of Exclusion Type Process in Dimension d ≥ 2.
    Journal of Applied Probability, 49.2, p.333-351, 2011.
    Link to journal

  • T. Franco, C. Landim, Hydrodynamic Limit of Gradient Exclusion Processes with Conductances.
    Archive for Rational Mechanics and Analysis, v.195, p.409 - 439, 2010.
    Link to journal
Research Group
Surveys, proceedings and chapters of books
  • T. Franco, P. Gonçalves, A. Neumann. Equilibrium fluctuations for the slow boundary exclusion process.
    From Particle Systems to Partial Differential Equations IV. Springer Proceedings in Mathematics & Statistics, 2017.
    Link
    PDF

  • A. Baraviera, T. Franco, A. Neumann. Hydrodynamic limit of quantum random walks. From Particle Systems to Partial Differential Equations III. Springer Proceedings in Mathematics & Statistics Volume 162, 2016, pp 39-50.
    Link
    PDF

  • T. Franco. Interacting particle systems: hydrodynamic limit versus high density limit. From Particle Systems to Partial Differential Equations. Springer Proceedings in Mathematics & Statistics Volume 75, 2014, pp 179-189.
    Link
    PDF

  • T. Franco, P. Gonçalves, A. Neumann. Slowed exclusion process: hydrodynamics, fluctuations and phase transitions. From Particle Systems to Partial Differential Equations. Springer Proceedings in Mathematics & Statistics Volume 75, 2014, pp 191-205.
    Link
    PDF

  • Lucas Melo, Messias Bittencourt, Gustavo Figueiredo, Tertuliano Franco. Seleção de paradigmas em redes ópticas híbridas integradas. Aceito para publicação no 31º Simpósio Brasileiro de Redes de Computadores e Sistemas Distribuídos, 2013.
    Link
    Página do evento

  • Franco, T., Gonçalves, P. and Neumann, A.: Dynamical phase transition in slowed exclusion processes. Modeling, Dynamics, Optimization and Bioeconomics I. Springer Proceedings in Mathematics & Statistics Volume 73, 2014, pp 269-278.
    • Link
    PDF

  • M. Cicconet, T. Franco and P. Carvalho. Plane Tessellation with Musical Scale Tiles and Bidimensional Automatic Composition.
    Proceedings of the International Computer Music Conference. New York, 2010.
    http://www.visgraf.impa.br/dmpm/
Books
  • T. Franco. Princípios de Combinatória e Probabilidade.
    Coleção Matemática Universitária, IMPA, 2021.
    Link

  • A mini-course in large deviations
    (notes of a lecture presented at Facultad de La República, Uruguay)
    Tertuliano Franco, 2015
    PDF

  • Banco de Questões OBMEP 2014.
    Autores: Tertuliano Franco (UFBA), Marcelo Hilário (UFMG), Johel Beltrán (PUCP), Jonathan Farfán (PUCP) e Alex Abreu (UFF)
    Disponível em PDF na página da OBMEP: http://www.obmep.org.br/banco.htm

  • Banco de Questões OBMEP 2013.
    Autores: Tertuliano Franco (UFBA), Marcelo Hilário (UFMG), Johel Beltrán (PUCP) e Jonathan Farfán (PUCP)
    Disponível em PDF na página da OBMEP: http://www.obmep.org.br/banco.htm

  • Introdução à Probabilidade só com Moedinhas.
    Tertuliano Franco, Marcelo Hilário, Pietro Silva. 1ª ed. Teresina: Universidade Federal do Piauí, 2012.
    Disponível em PDF: link

  • Banco de Questões OBMEP 2012.
    Autores: Tertuliano Franco (UFBA), Marcelo Hilário (UFMG) e Adriana Neumann (UFRGS)
    Disponível em PDF na página da OBMEP: http://www.obmep.org.br/banco.htm
Advising recomendations (in Portuguese)
Advising activies
  • Juan Carlos Arroyave Blanco (Master, 2021) Link

  • Eduardo Sampaio Pimenta (Master, 2021) Link

  • Diogo Soares Dórea da Silva (PhD, 2020) Link

  • Luana Amaral Gurgel (PhD, co-advised, 2020) Link

  • Mariana Tavares de Aguiar (PhD, 2019) Link

  • Pedro Paulo Gondim Cardoso (Master, 2017) Link

  • Luana Amaral Gurgel (Master, 2016) Link

  • Diogo Soares Dórea da Silva (Master, 2015) Link

  • Renata Issa Vianna (Master, 2015) Link

  • Ronei Badaró (ProfMat Program, 2015) Link

  • Cleber Assis (ProfMat Program, 2014) Link

  • Diego Daltro Conceição (Master, 2014) Link

  • Diogo Soares Dórea da Silva (Undergraduate Monograph, 2013) Link
Organization of Conferences:
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