Probability
Summary of the main advancements during the last 30 months
During this period there was an intense research activity in various topics in theoretical
probability and applications, in special to statistical mechanics. It deserves to be
mentioned the success obtained in the study of disordered systems, in particular in the
treatment of random walks in random environments, and growth models out of
equilibrium. Special emphasis merits the results which have been obtained in the
hydrodynamical description of particle systems, perfect simulation, convergence of
random trees to structures such as the Brownian web, interfaces of competition, besides
applications to linguistics.
Research articles published or accepted 2002-2004
During the period, the members of the team have had around fifty research articles
published or accepted for publication and a book, edited by the Cambridge University
Press.
It follows the list of the works, which considered being the most important for the area.
The full list is found in the reports sent by the various work groups.
1. Ferrari, P. A., Landim, C. and Thorisson, H., Poisson trees, succession lines and
coalescing random walks, Annales de L'Institut Henry Poincaré, 40, 141-152, 2004.
2. Fontes, L. R. G., Isopi, M., Newman, C. M. and Ravishankar, K., The Brownian Web:
Characterization and Convergence, Annals of Probability, 2004.
3. Machado, F. P., Alves, O. and Ferreira, C. E., Estimates for the spreading velocity of
an epidemic model, Mathematics and Computers in Simulation, 2004.
4. Olivieri, E. and Vares, M.E., Large Deviations and Metastability, Cambridge Univ.
Press, Encyclopedia of Mathematics and its applications, 512p, 2004.
5. Ramirez, A. F. and Sidoravicius, V., Asymptotic behavior of boundary branching
random walks growth process, J. Europ. Math. Soc. JEMS, 6 (3), 293-334, 2004.
6. Sidoravicius, V. and Sznitman, A.S., Quenched invariance principles for walks on
clusters of percolations or among random conductances, Probab. Theory. Rel.
Fields., 129(2), 2004.
7. Abadi, M., Sharp error terms and necessary conditions for exponential hitting times
in mixing processes, Annals of Probability, 2003.
8. Abadi, M. Chazottes, J.R.; Redig, F.; Verbitskiy E., Exponential distribution for the
occurrence of rare patterns in Gibbsian random fields, Comm. Math. Phys, 2003.
9. Comets, F. and Popov, S., Limit law for transition probabilities and moderate
deviations for Sinai's random walk in random environment, Probability Theory and
Related Fields, 126, 571-609, 2003.
10. Ferrari, P. A., Andjel, E. D. and Siqueira, A., Law of large numbers for the
asymmetric simple excusion process, Stochastic Processes and their Applications,
2003.
11. Garcia, N. and Motta, M.R., Perfect simulation for a stationary silo with absorbing
walls, Meth. Comp. Appl. Probab, 5, 109-121, 2003.
12. Machado, F.P. and Popov, S., Branching random walk in random environment on
trees, Stochastic Processes and their Applications, 106, 95-106, 2003.
13. Fernandez, R and Galves, A., Markov approximations of chains of infinite order, Bull.
Braz.Math.Soc., 33, 295-306, 2002.
14. Fontes, L. R., Schonmann, R. H. and Sidoravicius, V., Stretched exponential fixation
in stochastic Ising models at zero temperature, Comm. Math. Phys, 228(3), 495-518,
2002.
15. Kesten, H. and Sidoravicius, V., The spread of a rumor or infection in a moving
population, Annals of Probab. Math.PR/0312496.
Ph.D. Degree
1. Fernando Pigeard de Almeida Prado, 2004, IME-USP. Advisor: Vladimir Belitsky
2. Guillermo Tomás Tetzlaff, 2004, Departamento de Computacin, FCEyN, Universidad
de Buenos Aires. Advisor: Pablo Augusto Ferrari.
3. Leandro Pinto Pimentel, 2004, IMPA. Advisor: Vladas Sidoravicius.
4. Milton Jara, 2004, IMPA. Advisor: Claudio Landim.
5. Adriano Francisco Siqueira, 2003, IME-USP. Advisor: Luiz Renato Gonalves Fontes.
6. Bernardo Borges Nunes de Lima, 2003, IMPA, (Prêmio Aranda Ordaz). Advisor:
Vladas Sidoravicius.
7. Denise Duarte Scarpa Magalhães Alves, 2003, IME-USP. Advisor: Antonio Galves.
8. Glauco Valle da Silva Coelho, 2003, IMPA. Advisor: Claudio Landim.
9. Raquel Mariela Sued, 2003, IMPA, (Prêmio Aranda Ordaz).
Landim.
Advisor: Claudio
10. Valentim Sisko, 2003, IME-USP. Advisor: Pablo Augusto Ferrari.
How did the IM-AGIMB contributed to the achievement of the results in research,
as well on the formation of new researchers?
IM-AGIMB has promoted in an unprecedented way the participation of students in the
scientific life of the group in a very intense way. For instance, they were stimulated to
expose their work in the various scientific meetings, which were organized with the
presence of scientific leaderships in the related topics. This has guaranteed them to be
much more integrated in the efforts, which were happening, and to receive a wide but
constructive criticism of their work. Post-doctoral positions have also been crucial on
that, due to the exchange of experiences. In terms of the progress in mathematics
research, the conferences had a very positive effect together with the crucial impact that
seems to have come from the scientific visits, partially promoted by IM-AGIMB, which
definitely allowed the continuation and conclusion of scientific projects of much
relevance to the field.
Impact which the support of IM-AGIMB had in the scientific activities as the
promoter of conferences and visits of researchers (national and international).
IM-AGIMB has been extremely important for the success of the following workshops and
conferences, for allowing its planning and implementation in an exceptional scientific
level.
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The Editions VI, VII and VIII Brazilian School of Probability Brazilian School of
Probability, happening in 2002 (Ubatuba, SP), 2003(Angra dos Reis, RJ) and 2004
(Ubatuba, SP) respectively.
Workshop Disorder, Percolation, Random Walks, 18-19 de fevereiro de 2002, IMPA,
Rio de Janeiro, Brasil.
Percolation, Particle Systems and Random Media, 12-17 de janeiro de 2004,
Santiago de Chile. (Evento realizado em colaboração da PUC de Santiago do Chile
e do IMPA.)
Combinatorics, Probability and Computing, 12-14 de fevereiro, 2004, IMPA, Rio de
Janeiro, Brasil.
Brazilian Workshop on Mathematical Physics, 3-5 de março, 2004, IMPA, Rio de
Janeiro, Brasil.
IM-AGIMB has also been crucial for the participation of a large number of LatinAmerican researchers and students in the last editions of the Brazilian School of
Probability. This was exactly one of our major difficulties before the IM-AGIMB. It has
also allowed that students already initiated in research and young researchers would
attend the workshop ``Percolation, Particle Systems and Random Media", an occasion
when they had the opportunity not only to explain their own work, but also to learn from
the informal and formal discussions with some of the highest level specialists in the
topic. The existence of IM-AGIMB is, no doubt, profoundly changing the possibilities of
interaction in Latin America. Another example, besides the Workshop done in
collaboration with PUC from Santiago, is the "Encontro em Probabilidade e Estatística
Matemática" which will happen in Buenos Aires at the end of this September, as well as
most of the flow of researchers between Brasil, Uruguai, Argentina and Chile, which is
visible in the scientific projects which had been developed (as shown in the list of
publications).
We plan to extend this interaction in the next "summer school at IMPA", with the
participation of a researcher from Universidad Nacional de Mexico, and also by a
stronger interaction with colleagues from Venezuela (Summer School in Merida, in
September of 2005). This experience also offers to the students the opportunity to wide
their vision of the area beyond the research lines that are most developed in their own
institution.
Concerning the collaboration through scientific visits, the results reported in the research
articles speak by themselves. Besides, there is an intense activity going on relative to
articles under preparation. The financial resources provided by other national sources
has also contributed much for the success of the scientific cooperation in the area.