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Stochastic modeling of interacting systems

Grant number: 09/52379-8
Support type:Research Projects - Thematic Grants
Duration: November 01, 2009 - October 31, 2015
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics
Principal Investigator:Fabio Prates Machado
Grantee:Fabio Prates Machado
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Co-Principal Investigators:Fabio Prates Machado ; Serguei Popov ; Vladimir Belitsky
Associated grant(s):15/06321-9 - Random walks and growth models, AV.EXT
13/04918-2 - Self-repelling random walks, stochastic dynamical systems, growth models, AV.EXT
12/07166-9 - Random walks in random environments, AV.EXT
+ associated grants 11/21089-4 - Large deviation properties of the ASEP with random rates, AV.EXT
11/07000-0 - Random walks and related topics, AV.EXT
10/16085-7 - Random walks in random environment, AV.EXT - associated grants
Associated scholarship(s):14/06998-6 - Random walks and growth models, BE.PQ
14/06815-9 - Random walks and other stochastic systems on graphs, BE.PQ
13/23081-6 - Percolation and random walks in dependent environments, BP.DD
+ associated scholarships 13/00855-6 - Random interlacements and the soft local times technique, BP.IC
12/01432-9 - Aging in the GREM-like trap model, BP.PD
10/06967-2 - Random walk systems and their applications to models of information diffusion, BP.PD
09/18253-7 - Stochastic modeling for population biology, BE.PQ - associated scholarships

Abstract

The present project originates in the previous 'projetos temáticos': Stochastic modeling of interacting systems (October 2004 to October 2008), Dynamical phase transitions in evolutionary systems, Large deviations, diffusion and localization (June 1991 to August 1994) and Critical phenomena in evolutionary processes and equilibrium systems (in two editions, from August 1995 to August 1998, and from July 2000 to June 2004). They all were highly succesful and triggered a remarkable increase in the level of activity, prestige and recognition of the particle-systems group of USP and UNICAMP. The research activities for the next five-year period will be focused on central topics of the theory of probability, statistical mechanics and related areas. Among them we mention: Properties of various stochastic processes and fields, percolation, interacting particle systems, convergence to equilibrium, random networks, processes in random environment, disordered systems, stochastic models in finance and risk assessment, scaling limit and aging of dynamics of disordered systems, stochastic clusters, quantum gravitation, gene expression systems, statistical genomics. As the previous 'projetos temáticos', the present project has three well defined goals: 1) to foster and strengthen the collaboration among researchers in the areas of project; 2) to promote contact with researchers of related areas or areas that may benefit from the expertise of the project team, and 3) to actively participate in the formation of new researchers. To achieve these goals, besides the specific research activities the following activities are proposed: a) scientific interchanges with Brazilian and foreign institutions; b) weekly seminars, with the participation of members of the project team and invited researchers; c) scientific meetings, and d) formation and advice of undergraduate students (orientação científica), master and PhD. students, and supervision of post-doctoral fellows. (AU)

Scientific publications (31)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
MACHADO, F. P.; ROLDAN-CORREA, A.; SCHINAZI, R. B. Colonization and Collapse. ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, v. 14, n. 2, p. 719-731, 2017. Web of Science Citations: 1.
VARGAS JUNIOR, VALDIVINO; MACHADO, FABIO PRATES; ROLDAN-CORREA, ALEJANDRO. Dispersion as a Survival Strategy. Journal of Statistical Physics, v. 164, n. 4, p. 937-951, AUG 2016. Web of Science Citations: 2.
COMETS, FRANCIS; POPOV, SERGUEI; VACHKOVSKAIA, MARINA. Two-Dimensional Random Interlacements and Late Points for Random Walks. Communications in Mathematical Physics, v. 343, n. 1, p. 129-164, APR 2016. Web of Science Citations: 3.
COLETTI, CRISTIAN F.; MIRANDA, DANIEL; MUSSINI, FILIPE. Invariance Under Quasi-isometries of Subcritical and Supercritical Behavior in the Boolean Model of Percolation. Journal of Statistical Physics, v. 162, n. 3, p. 685-700, FEB 2016. Web of Science Citations: 0.
LEBENSZTAYN, ELCIO; MACHADO, FABIO PRATES; MARTINEZ, MAURICIO ZULUAGA. Random Walks Systems with Finite Lifetime on Z. Journal of Statistical Physics, v. 162, n. 3, p. 727-738, FEB 2016. Web of Science Citations: 1.
GONZALEZ-NAVARRETE, MANUEL; PECHERSKY, EUGENE; YAMBARTSEV, ANATOLY. Phase Transition in Ferromagnetic Ising Model with a Cell-Board External Field. Journal of Statistical Physics, v. 162, n. 1, p. 139-161, JAN 2016. Web of Science Citations: 0.
BELITSKY, V.; MENSHIKOV, M.; PETRITIS, D.; VACHKOVSKAIA, M. Random Dynamical Systems with Systematic Drift Competing with Heavy-Tailed Randomness. Markov Processes and Related Fields, v. 22, n. 4, p. 629-652, 2016. Web of Science Citations: 0.
COMETS, F.; GALLESCO, C.; POPOV, S.; VACHKOVSKAIA, M. Constrained Information Transmission on Erdos - Renyi Graphs. Markov Processes and Related Fields, v. 22, n. 1, p. 111-138, 2016. Web of Science Citations: 1.
GREJO, CAROLINA; MACHADO, FABIO; ROLDAN-CORREA, ALEJANDRO. The fitness of the strongest individual in the subcritical GMS model. Electronic Communications in Probability, v. 21, 2016. Web of Science Citations: 0.
BARRETO-SOUZA, W.; FONTES, L. R. G. Long-range Trap Models on and Quasistable Processes. JOURNAL OF THEORETICAL PROBABILITY, v. 28, n. 4, p. 1500-1519, DEC 2015. Web of Science Citations: 1.
FONTES, LUIZ RENATO; MARCHETTI, DOMINGOS H. U.; MEROLA, IMMACOLATA; PRESUTTI, ERRICO; VARES, MARIA EULALIA. Layered Systems at the Mean Field Critical Temperature. Journal of Statistical Physics, v. 161, n. 1, p. 91-122, OCT 2015. Web of Science Citations: 3.
DE BERNARDINI, DIEGO F.; POPOV, SERGUEI. Russo's Formula for Random Interlacements. Journal of Statistical Physics, v. 160, n. 2, p. 321-335, JUL 2015. Web of Science Citations: 0.
POPOV, SERGUEI; RATH, BALAZS. On Decoupling Inequalities and Percolation of Excursion Sets of the Gaussian Free Field. Journal of Statistical Physics, v. 159, n. 2, p. 312-320, APR 2015. Web of Science Citations: 14.
FONTES, LUIZ RENATO; ALEXANDER VALENCIA, LEON; VALLE, GLAUCO. Scaling limit of the radial Poissonian web. ELECTRONIC JOURNAL OF PROBABILITY, v. 20, MAR 28 2015. Web of Science Citations: 0.
POPOV, SERGUEI; TEIXEIRA, AUGUSTO. Soft local times and decoupling of random interlacements. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, v. 17, n. 10, p. 2545-2593, 2015. Web of Science Citations: 15.
FONTES, LUIZ RENATO; MARCHETTI, DOMINGOS H. U.; MEROLA, IMMACOLATA; PRESUTTI, ERRICO; VARES, MARIA EULALIA. Phase Transitions in Layered Systems. Journal of Statistical Physics, v. 157, n. 3, p. 407-421, NOV 2014. Web of Science Citations: 4.
COLETTI, CRISTIAN; VALLE, GLAUCO. Convergence to the Brownian Web for a generalization of the drainage network model. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, v. 50, n. 3, p. 899-919, AUG 2014. Web of Science Citations: 1.
MOGULSKII, A.; PECHERSKY, E.; YAMBARTSEV, A. Large deviations for excursions of non-homogeneous Markov processes. Electronic Communications in Probability, v. 19, p. 1-8, JUN 22 2014. Web of Science Citations: 0.
FONTES, L. R. G.; MATHIEU, P. On the dynamics of trap models in Z(d). PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, v. 108, n. 6, p. 1562-1592, JUN 2014. Web of Science Citations: 6.
MENSHIKOV, MIKHAIL; POPOV, SERGUEI. On Range and Local Time of Many-dimensional Submartingales. JOURNAL OF THEORETICAL PROBABILITY, v. 27, n. 2, p. 601-617, JUN 2014. Web of Science Citations: 4.
FONTES, L. R. G.; GAVA, R. J.; GAYRARD, V. THE K-PROCESS ON A TREE AS A SCALING LIMIT OF THE GREM-LIKE TRAP MODEL. ANNALS OF APPLIED PROBABILITY, v. 24, n. 2, p. 857-897, APR 2014. Web of Science Citations: 2.
BERTACCHI, DANIELA; MACHADO, FABIO PRATES; ZUCCA, FABIO. LOCAL AND GLOBAL SURVIVAL FOR NONHOMOGENEOUS RANDOM WALK SYSTEMS ON Z. ADVANCES IN APPLIED PROBABILITY, v. 46, n. 1, p. 256-278, MAR 2014. Web of Science Citations: 3.
AMSALU, S.; HAUSER, R.; MATZINGER, H. A Monte Carlo Approach to the Fluctuation Problem in Optimal Alignments of Random Strings. Markov Processes and Related Fields, v. 20, n. 1, p. 107-144, 2014. Web of Science Citations: 1.
GALLESCO, C.; GANTERT, N.; POPOV, S.; VACHKOVSKAIA, M. A Conditional Quenched CLT for Random Walks Among Random Conductances on Z(d). Markov Processes and Related Fields, v. 20, n. 2, p. 287-328, 2014. Web of Science Citations: 0.
PERES, YUVAL; POPOV, SERGUEI; SOUSI, PERLA. On recurrence and transience of self-interacting random walks. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 44, n. 4, p. 841-867, DEC 2013. Web of Science Citations: 5.
COMETS, FRANCIS; GALLESCO, CHRISTOPHE; POPOV, SERGUEI; VACHKOVSKAIA, MARINA. On large deviations for the cover time of two-dimensional torus. ELECTRONIC JOURNAL OF PROBABILITY, v. 18, p. 1-18, NOV 6 2013. Web of Science Citations: 7.
MENSHIKOV, M. V.; SISKO, V. V.; VACHKOVSKAIA, M. Introduction to Shape Stability for a Storage Model. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, v. 15, n. 1, p. 125-146, MAR 2013. Web of Science Citations: 0.
GALLESCO, CHRISTOPHE; POPOV, SERGUEI; SCHUETZ, GUNTER M. Localization for a Random Walk in Slowly Decreasing Random Potential. Journal of Statistical Physics, v. 150, n. 2, p. 285-298, JAN 2013. Web of Science Citations: 1.
FONTES, L. R.; PEIXOTO, G. R. C. Elementary Results on K Processes with Weights. Markov Processes and Related Fields, v. 19, n. 2, p. 343-370, 2013. Web of Science Citations: 0.
GALLESCO, CHRISTOPHE; POPOV, SERGUEI. Random walks with unbounded jumps among random conductances II: Conditional quenched CLT. ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, v. 10, n. 1, p. 253+, 2013. Web of Science Citations: 2.
BEZERRA, S. C.; FONTES, L. R. G.; GAVA, R. J.; GAYRARD, V.; MATHIEU, P. Scaling limits and aging for asymmetric trap models on the complete graph and K processes. ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, v. 9, n. 2, p. 303-321, 2012. Web of Science Citations: 4.

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