Submitted papers in international journals:
[79.] Gonçalves, P., Salvador, B. (2024): On the correlations of some microscopic random systems, submitted.
[78.] Gonçalves, P., Hayashi, K. , Sasada, M. (2024): Characterization of Gradient Condition for Asymmetric Partial Exclusion Processes and Their Scaling Limits, submitted and online at arxiv.org.
[77.] Gonçalves, P., Nahum, G., Simon, M. (2023): From Exclusion to Slow and Fast Diffusion, submitted and online at arxiv.org.
Accepted papers in international journals:
[76.] Cannizzaro, G., Gonçalves, P., Misturini, R., Occelli, A. (20223): From ABC to KPZ, accepted for publication in PTRF.
[75.] Araujo, O., Gonçalves, P., Simas, A. (2023): Hydrodynamic limit of the multi-component slow boundary WASEP with collisions, accepted for publication in ALEA.
[74.] Cardoso, P., Gonçalves, P., Jimenez-Oviedo, B. (2023): Hydrodynamics of a d-dimensional long jumps symmetric exclusion with a slow barrier, accepted for publication in AIHP, Prob & Stats.
[73.] De Carlo, L. Gabrielli, D., Gonçalves, P. (2021): Hydrodynamic Limit of an exclusion process with vorticity, to appear in AIHP, Prob & Stats.
[72.] Cardoso, P., Gonçalves, P., Jiménez-Oviedo, B. (2022): Hydrodynamic behavior of long-range symmetric exclusion with a slow barrier: superdiffusive regime, to appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze.
[71.] Gonçalves, P., Jara, M., Menezes, O., Marinho, R. (2022): Sharp convergence to equilibrium for the SSEP with reservoirs, to appear in AIHP, Prob & Stats.
Published papers in international journals:
[70.] Franceschini, C., Gonçalves, P., Jara, M., Salvador, B. (2024): Non-equilibrium fluctuations for SEP(α) with open boundary, Stochastic processes and their Applications, Volume 178, 104463.
[69.] Gonçalves, P., Jara, M., Menezes, O., Marinho, R. (2024): CLT for NESS of a reaction-diffusion model, Probability Theory and Related Fields, Volume 190, 337–377.
[68.] Cardoso, P., Gonçalves, P., Jiménez-Oviedo, B. (2024): Hydrodynamic behavior of long-range symmetric exclusion with a slow barrier: diffusive regime, AIHP, Prob & Stats, Volume 60, no. 3, 1511-1542.
[67.] Bernardin, C., Gonçalves, P., Olla, S. (2024): Space-time fluctuations in a quasi-static limit, Mathematical Physics Aanalysis and Geometry, Volume 27, no. 7, 1-19.
[66.] Gonçalves, P. (2023): On the universality from interacting particle systems, ICM 2022 proceedings, Volume VI, 4326-4349.
[65.] Gonçalves, P., Hayashi, K. (2023): Derivation of anomalous behavior from interacting oscillators in the high-temperature regime, Commun. Math. Phys., Volume 403, 1193–1243.
[64.] Cardoso, P., Gonçalves, P., Jimenez-Oviedo, B. (2023): Diffusive fluctuations of long-range symmetric exclusion with a slow barrier, Stochastic Processes and their Applications, Volume 166, 47 pages.
[63.] Bernardin, C., Cardoso, P., Gonçalves, P., Scotta, S. (2023): Hydrodynamic limit for a boundary driven super-diffusive symmetric exclusion, Stochastic Processes and their Applications, Volume 165, 43-95.
[62.] Gonçalves, P., Jara, Marinho, R., Moreira, D. (2023): Scaling Limits for Rudvalis Card Shuffles, Advances in Applied Mathematics, Volume 150, 1-32.
[61]. Gonçalves, P., Misturini, R., Occelli, A. (2023): Hydrodynamic for ABC with slow/fast boundary, Stochastic Processes and their Applications, Volume 161, 350-384.
[60.] Franceschini, C., Gonçalves, P., Salvador, B. (2023): Hydrodynamical behavior of generalized symmetric exclusion with open boundary, MPAG, Volume 26, issue 2, 1-23.
[59.] Franco, T., Gonçalves, P., Neumann, A. (2023): Large Deviations for the SSEP with slow boundary: the non-critical case, ALEA Lat. Am. J. Probab. Math. Stat., no. 20, 359–394.
[58.] Cardoso, P., De Paula, R., Gonçalves, P. (2023): Derivation of the fractional porous medium equation from a microscopic dynamic, Nonlinearity, Volume 36, number 3, 1840–1872.
[57.] Franco, T., Gonçalves, P., Landim, C., Neumann, A. (2022): Dynamical large deviations for the boundary driven symmetric exclusion process with Robin boundary conditions, ALEA Lat. Am. J. Probab. Math. Stat., Volume 19, no. 2, 1497-1546.
[56.] Bernardin, C., Gonçalves, P., Jiménez-Oviedo, B. and Scotta, S. (2022): Non-equilibrium stationary properties of the boundary driven zero-range process with long jumps, JSP, Volume 189, article 32.
[55.] Ahmed, R., Bernardin, C., Gonçalves, P., Simon, M. (2022): A microscopic derivation of coupled SPDE's with a KPZ flavor, AIHP, Prob & Stats, Volume 58, No. 2, 890–915.
[54.] Gonçalves, P., Scotta, S. (2022): Diffusive to super-diffusive behavior in boundary driven exclusion, Markov Processes and Related Fields, Volume 28, 149-178.
[53.] Franceschini, C., Gonçalves, P., Sau, F. (2022): Symmetric inclusion process with slow boundary: hydrodynamics and hydrostatics, Bernoulli, Volume 28, Issue 2, 1340-1381.
[52.] Bernardin, C., Gonçalves, P., Jara, M., Scotta, S. (2022): Equilibrium fluctuations for diffusive symmetric exclusion with long jumps and infinitely extended reservoirs, AIHP, Prob & Stats, Volume 58, Issue 1, 303-342.
[51.] De Paula, R., Gonçalves, P., Neumann, A. (2021): Energy estimates and convergence of weak solutions of the porous medium equation, Nonlinearity, Volume 34, 7872-7915.
[50.] Amir, G., Busani, O., Gonçalves, P., Martin, J. (2021): The TAZRP speed process, AIHP, Prob & Stats., Volume 57, Issue 3, 1281-1305.
[49]. Gonçalves, P. and Occelli, A. (2021): On Energy solutions to Stochastic Burgers equation, MPRF, Volume 27, 523-556.
[48.] Chen, J., Gonçalves, P. (2021): Asymptotic behavior of density in the boundary-driven exclusion process on the Sierpinski gasket, Mathematical Physics Analysis and Geometry, Volume 24, issue 3, article 24.
[47.] Bernardin, C., Gonçalves, P., Jiménez-Oviedo, B. (2021): A microscopic model for the regional fractional Laplacian with Dirichlet boundary conditions, Archive for Rational Mechanics and Analysis, Volume 239, 1-48.
[46.] Erignoux, C., Gonçalves, P., Nahum, G.. (2020): Hydrodynamics for SSEP with non-reversible slow boundary dynamics: Part I, the critical regime and beyond, Journal of Statistical Physics, Volume 181, Issue 4, 1433-1469.
[45.] Erignoux, C., Gonçalves, P., Nahum, G.. (2020): Hydrodynamics for SSEP with non-reversible slow boundary dynamics: Part II, the critical regime and beyond, ALEA, Lat. Am. J. Probab. Math. Stat., Volume 17, 791–823, http://alea.impa.br/articles/v17/17-31.pdf.
[44.] Gonçalves, P., Jara, M., Neumann, A., Menezes, O. (2020): Non-equilibrium and stationary fluctuations for a slowed boundary symmetric exclusion, Stochastic Processes and their Applications, Volume 130, Issue 7, 4326-4357.
[43.] Bonorino, L., De Paula, R., Gonçalves, P., Neumann, A. (2020): Hydrodynamics for the porous medium model with slow reservoirs, Journal of Statistical Physics, Volume 179, 748-788.
[42.] Anwasia, B., Gonçalves, P., Soares, A.J. (2020): On the formal derivation of the reactive Maxwell-Stefan equations from the kinetic theory, European Physics Letters, 129, 40005, 1-7.
[41.] Erhard, D., Franco, T., Gonçalves, P., Neumann, A. and Tavares, M. (2020): Non-equilibrium fluctuations for the SSEP with a slow bond, in Annales de l'Institut Henri Poincaré: Probability and Statistics, Volume 56, Issue 2, 1099-1128.
[40.] Gonçalves, P., Perkowski, N. and Simon, M. (2020): Derivation of the Stochastic Burgers equation with Dirichlet boundary conditions from the WASEP, Annales Henri Lebesgue, Volume 3, 87-167.
[39.] Anwasia, B., Gonçalves, P. and Soares, A.J. (2019): From the simple reaction sphere kinetic model to the reaction-diffusion system of Maxwell-Stefan type, Communications in Mathematical Sciences, Volume 17, Issue 2, 507-538.
[38.] Gonçalves, P. (2019): Hydrodynamics for symmetric exclusion in contact with reservoirs, Stochastic Dynamics Out of Equilibrium, Institut Henri Poincaré, Paris, France, 2017, Springer Proceedings in Mathematics and Statistics book series, 137-205.
[37.] Bernardin, C., Gonçalves, P. and Jiménez-Oviedo, B. (2019): Slow to fast infinitely extended reservoirs for the symmetric exclusion process with long jumps, Markov Processes and Related Fields, Volume 25, 217-274.
[36.] Gonçalves, P. and Jara, M. (2019): Quadratic fluctuations of the simple exclusion, ALEA, Issue 16, 605-632.
[35.] Franco, T., Gonçalves, P. and Neumann, A. (2019): Non-equilibrium and stationary fluctuations for a slowed boundary symmetric exclusion process, Stochastic Processes and their Applications, Volume 129, Issue 4, 1413-1442.
[34.] Bernardin, C., Gonçalves, P., Jara, M., Simon, M. (2018): Interpolation process between standard diffusion and fractional diffusion, Annales de l'Institut Henri Poincaré: Probability and Statistics, Volume 54, Issue 3, 1731-1757.
[33.] Bernardin, C., Gonçalves, P., Jara, M. and Simon, M. (2018): Nonlinear perturbation of a noisy Hamiltonian lattice field model: universality persistence, Communications in Mathematical Physics, Volume 361, Issue 2, 605-659.
[32.] Bernardin, C., Gonçalves, P., Jara, M. (2018): Weakly harmonic oscillators perturbed by a conserving noise, Annals of Applied Probability, Volume 28, Issue 3, 1315-1355.
[31.] Gonçalves, P., Jara, M. (2018): Density fluctuations for exclusion processes with long jumps, in Probability Theory and Related Field, Volume 170, Issue 1–2, 311-362.
[30.] Gonçalves, P., Jara, M. (2017): Stochastic Burgers equation from long range exclusion interactions, Stochastic Processes and their applications, Volume 127, Issue 12, 4029-4052.
[29.] Gonçalves, P., Landim, C., Milanes, A. (2017): Nonequilibrium fluctuations of one-dimensional boundary driven weakly asymmetric exclusion processes, The Annals of Applied Probability, Volume 27, Issue 1, 140–177.
[28.] Gonçalves P., Jara, M., Simon, M. (2017): Second order Boltzmann-Gibbs Principle for polynomial functions and applications, Journal of Statistical Physics, Volume 166, Issue 1, 90–113.
[27.] Blondel, O., Gonçalves, P., Simon, M. (2016): Convergence to the Stochastic Burgers equation from a degenerate microscopic dynamics, Electronic Journal of Probability, Volume 21, Issue 69, 1-26.
[26] Franco, T., Gonçalves, P., Neumann, A. (2016): Corrigendum to: Phase transition in equilibrium fluctuations of symmetric slowed exclusion, Stochastic Processes and their applications, Volume 126, Issue 10, 3235-3242.
[25.] Bernardin, C., Gonçalves, P., Sethuraman, S. (2016): Occupation times of long-range exclusion and connections to KPZ class exponents, Probability Theory and Related Fields, Volume 166, Issue 1, 365-428.
[24.] Franco, T., Gonçalves, P., Simon, M. (2016): Crossover to the Stochastic Burgers Equation for the WASEP with a slow bond, Communications in Mathematical Physics, Volume 346, Issue 3, 801-838.
[23.] Bernardin, C., Gonçalves, P., Jara, M. (2016): 3/4-Fractional superdiffusion in a system of harmonic oscillators perturbed by a conservative noise, Archive for Rational Mechanics and Analysis, Volume 220, Issue 2, 505 - 542.
[22.] Franco, T., Gonçalves, P., Schutz, G. (2016): Scaling limits for the exclusion process with a slow site, Stochastic Processes and their applications, Volume 126, Issue 3, 800 - 831.
[21.] Franco, T., Gonçalves, P., Neumann, A. (2015): Phase transition of a Heat equation with Robin's boundary conditions and exclusion process, Transactions of the American Mathematical Society, Volume 367, Issue 9, 6131 - 6158.
[20.] Bernardin, C., Gonçalves, P., Jara, M., Sasada, M., Simon, M. (2015): From normal diffusion to superdiffusion of energy in the evanescent flip noise limit, Journal of Statistical Physics, Volume 159, Issue 6, 1327 - 1368.
[19.] Gonçalves, P., Jara, M. (2015): The Einstein relation for the KPZ equation, Journal of Statistical Physics, volume 158, Issue 6, 1262 - 1270.
[18.] Gonçalves, P., Jara, M., Sethuraman, S. (2015): A stochastic Burgers equation from a class of microscopic interactions, Annals of Probability, volume 43, Issue 1, 286 - 338.
[17.] Franco, T., Gonçalves, P., Neumann, A. (2014): Occupation times of exclusion processes with conductances, Journal of Statistical Physics, volume 156, Issue 5, 975 - 997.
[16.] Gonçalves, P., Jara, M. (2014): Nonlinear fluctuations of weakly asymmetric interacting particle systems, Archive for Rational Mechanics and Analysis, Volume 212, Issue 2, 597 - 644.
[15.] Gonçalves, P. (2014): On the asymmetric zero-range in the rarefaction fan, Journal of Statistical Physics, Volume 154, Issue 4, 1074 - 1095.
[14.] Bernardin, C., Gonçalves, P., Landim, C. (2014): Entropy of non-equilibrium stationary measures of boundary-driven TASEP, Journal of Statistical Physics, Volume 154, Issue 1-2, 378 - 420.
[13.] Bernardin, C., Gonçalves, P. (2014): Anomalous Fluctuations for a Hamiltonian system with exponential interactions, Communications in Mathematical Physics, Volume 325, Issue 1, pp 291 - 332.
[12.] Franco, T., Gonçalves, P., Neumann, A. (2013): Phase transition in equilibrium fluctuations of symmetric slowed exclusion, Stochastic Processes and their Applications, 123, Issue 12, 4156 – 4185.
[11.] Franco, T., Gonçalves, P., Neumann, A. (2013): Hydrodynamical behavior of symmetric exclusion with slow bonds, Annales de l'Institut Henri Poincaré: Probability and Statistics, Volume 49, Number 2, 402 - 427.
[10.] Gonçalves, P., Jara, M. (2013): Scaling limits of additive functionals of interacting particle systems, Communications on Pure and Applied Mathematics, Volume 66, Issue 5, 649 - 677.
[9.] Gonçalves, P., Jara, M. (2012): Crossover to the KPZ equation, Annales Henri Poincaré, Volume 13, Number 4, 813 - 826.
[8.] Gonçalves, P. (2011): A hyperbolic conservation law and Particle Systems, Journal of Difference Equations and Applications, Volume 17, Issue 8, 1207 - 1217.
[7.] Gonçalves, P. (2010): Equilibrium Fluctuations for the Totally Asymmetric Zero-Range Process, Journal of Statistical Physics, Volume 138, nº4-5, 645 - 661.
[6.] Gonçalves, P.; Jara, M. (2009): Density Fluctuations for a zero-range process on the percolation cluster, Electronic Communications in Probability, 14, 382 - 395.
[5.] Gonçalves, P.; Landim, C., Toninelli, C. (2009): Hydrodynamic Limit for a Particle System with degenerate rates, Annales de l'Institut Henri Poincaré: Probability and Statistics, Volume 45, nº4, 887 - 909.
[4.] Ferrari, P.; Gonçalves, P., Martin, J. (2009): Collision probabilities in the rarefaction fan of asymmetric exclusion processes, Annales de l'Institut Henri Poincaré: Probability and Statistics, Volume 45, nº4, 1048 - 1064.
[3.] Gonçalves, P., Jara, M. (2008): Scaling Limits of a Tagged Particle in the Exclusion Process with Variable Diffusion Coefficient, Journal of Statistical Physics, 132, nº6, 1135 - 1143.
[2.] Gonçalves, P., Jara, M. (2008): Scaling limits for gradient systems in random environment, Journal of Statistical Physics, 131, nº4, 691 - 716.
[1.] Gonçalves, P. (2008): Central Limit Theorem for a Tagged Particle in Asymmetric Simple Exclusion, Stochastic Processes and their Applications, 118, 474 - 502.
Publications at Conference proceedings with referee:
[7.] Cardoso, P., Gonçalves, P., Linear and Nonlinear Fractional PDEs from interacting particle systems, accepted for publication.
[6.] Gonçalves, P.: Derivation of the KPZ equation from particle systems, European Mathematical Society - Publishing House, Report No. 55/2014 of the conference "KPZ equation:: around its universality class" at the Mathematisches Forschungsinstitut - Oberwolfach.
[5.] Gonçalves, P. (2014): Phase transitions on the scaling limits of the symmetric slowed exclusion, European Mathematical Society - Publishing House, Report No. 52/2013 of the conference "Large Scale Stochastic Dynamics" at the Mathematisches Forschungsinstitut - Oberwolfach.
[4.] Jara, M., Gonçalves, P. (2010): Universality of KPZ equation and renormalization techniques in interacting particle systems, at the Report No. 50/2010 of the conference "Large Scale Stochastic Dynamics" at the Mathematisches Forschungsinstitut - Oberwolfach.
[3.] Gonçalves, P., Jara, M. (2010): The crossover to the KPZ equation, Report No. 50/2010 of the conference "Large Scale Stochastic Dynamics" at the Mathematisches Forschungsinstitut - Oberwolfach.
[2.] Gonçalves, P., Jara, M. (2010): Crossover to the KPZ equation, Conference proceedings of the "5th International Workshop on Applied Probability''.
[1.] Ferrari, P., Gonçalves, P., Martin, J. (2007): Second and Third Class particles in TASEP, Report No.42/2007 of the conference "Large Scale Stochastic Dynamics" at the Mathematisches Forschungsinstitut - Oberwolfach, available online at www.mfo.de.
Book Chapters:
[12] Birmpa, P., Gonçalves, P., Tsagkarogiannis, D. (2021): On non-equilibrium fluctuations for the Stirring process with births and deaths, Particle Systems and Partial Differential Equations VI, VII and VIII, Springer Proceedings in Mathematics & Statistics.
[11.] Capitão, P., Gonçalves, P. (2021): Hydrodynamics of weakly asymmetric exclusion with slow boundary, Particle Systems and Partial Differential Equations VI, VII and VIII, Springer Proceedings in Mathematics & Statistics.
[10.] Gonçalves, P., Neumann, A. and Paula, R. (2017): The Porous medium model in contact with slow reservoirs, Particle Systems and Partial Differential Equations V, ed. A.J. Soares and P. Gonçalves, Springer Proceedings in Mathematics & Statistics.
[9.] Franco, T., Gonçalves, P. and Neumann, A. (2016): Equilibrium fluctuations for the slow boundary exclusion process, to appear in Particle Systems and Partial Differential Equations IV, ed. A. J. Soares and P. Gonçalves, Springer Proceedings in Mathematics & Statistics, Volume 209, pp. 177 - 197.
[8.] Gonçalves, P. (2015): Derivation of the Stochastic Burgers Equation from the WASEP,
Particle Systems and Partial Differential Equations II, ed. A. J. Soares and P. Gonçalves, Springer Proceedings in Mathematics & Statistics, Volume 129, pp 209 - 229.
[7.] Gonçalves, P. (2014): Exclusion and zero-range in the rarefaction fan, Particle Systems and Partial Differential Equations, ed. C. Bernardin and P. Gonçalves, Springer Proceedings in Mathematics & Statistics Volume 75, pp 207 - 224.
[6.] Bernardin, C., Gonçalves, P. and Sethuraman, S. (2014): Equilibrium fluctuations of additive functionals of zero-range models, Particle Systems and Partial Differential Equations, ed. C. Bernardin and P. Gonçalves, Springer Proceedings in Mathematics & Statistics Volume 75, pp 143 - 160.
[5.] Franco, T., Gonçalves, P. and Neumann, A. (2014): Slowed exclusion process: hydrodynamics, fluctuations and phase transitions, Particle Systems and Partial Differential Equations, ed. C. Bernardin and P. Gonçalves, Springer Proceedings in Mathematics & Statistics Volume 75, pp 191 - 205.
[4.] Franco, T., Gonçalves, P. and Neumann, A. (2014): Dynamical phase transition in slowed exclusion processes, Modeling, Dynamics, Optimization and Bioeconomics I, Springer Proceedings in Mathematics & Statistics Volume 73, pp 269 - 278.
[3.] Gonçalves, P. (2014): Occupation times of exclusion processes, Modeling, Dynamics, Optimization and Bioeconomics I, Springer Proceedings in Mathematics & Statistics Volume 73, 2014, pp 329 - 341.
[2.] Gonçalves, P. (2011): Simple Exclusion Process: from randomness to determinism, Dynamics, Games and Science I, ed. M. Peixoto, A. Pinto and D. Rand, Springer Proceedings in Mathematics, 391 - 404.
[1.] Gonçalves, P. (2011): Microscopic dynamics for the porous medium equation, Dynamics, Games and Science II, ed. M. Peixoto, A. Pinto and D. Rand, Springer Proceedings in Mathematics, 387 - 392.
Other publications:
[6.] Gonçalves, P. (2023): Hydrodynamic limits: the emergence of fractional boundary conditions, Eur. Math. Soc. Mag., no. 127, 5–14.
[5.] Franceschini, C., Gonçalves, P. (2020): Where Lie Algebra meets Probability?!, Bulletin CIM - "Centro Internacional da Matemática", nº 42, 11-21.
[4.] Brito, I., Gonçalves, P., Ramos. P. (2017): O risco na atividade seguradora, Boletim da Sociedade Portuguesa de Matemática, 75, 3-33.
[3.] Gonçalves, P., Oviedo, B. (2015): Processo de exclusão simples e a equação do calor, submitted for publication.
[2.] Gonçalves, P. (2013): Funcionais aditivos de processos de exclusão, Boletim da Sociedade Portuguesa de Matemática, Actas do Encontro Nacional da Sociedade Portuguesa de Matemática, Faro, Julho de 2012, 163-166.
[1.] Gonçalves, P. (2009): Hydrodynamic Limit of Particle Systems, Bulletin CIM - "Centro Internacional da Matemática", nº 26, 12-18.
PhD Thesis:
Gonçalves, P. (2007): Central Limit Theorem for a Tagged Particle in Asymmetric Simple Exclusion and Hydrodynamic Limit for a Particle System with Degenerate Rates, IMPA Ph.D. thesis (2007).
Books and Lecture notes:
[5.] Gonçalves, P. (2021): "Notas em teoria da medida".
[4.] Gonçalves, P. (2017): "Hydrodynamics for symmetric exclusion in contact with reservoirs",
Springer Lecture Notes in Mathematics.
[3.] Gonçalves, P. (2017): "Probability theory: an introduction", online at
https://fenix.tecnico.ulisboa.pt/disciplinas/TP251795/2017-2018/1-semestre/new-entry-894.
[2.] Brito, I., Gonçalves, P. (2015): "Introdução à Teoria do Risco", online at
http://hdl.handle.net/1822/35761.
[1.] Gonçalves, P. (2010): "Equilibrium Fluctuations for Totally Asymmetric Particle Systems", VDM Verlag Dr. Müller e.K., ISBN: 978-3-639-09575-3, paperback, 200 Pages.