[ABE-L] COLMEA -=?ISO-8859-1?Q?_col=F3quio_interins?=titucional - dia 28/10 - no IMPA

[Maria Eulalia Vares]

Prezados colegas,

No próximo dia 28 teremos, no IMPA, um novo encontro do COLMEA - Colóquio
Interinstitucional "Modelos Estocásticos e Aplicações".

Programa:

14:00 - 15:20h: Patrick Cattiaux (Univ. Toulouse)

"About some stochastic models on collective behaviour"

15:40 - 17:00h: Hubert Lacoin (IMPA)

"Disorder relevance for pinning of random surfaces"

17:00 h: Discussão e lanche

Local: Auditório Ricardo Mañé - IMPA
Estrada Dona Castorina, 110
Rio de Janeiro

Um cartaz para divulgação encontra-se aqui:

http://www.im.ufrj.br/~coloquiomea/cartaz/2015_10.pdf

Informações mais completas sobre o COLMEA podem ser encontradas aqui:

http://www.im.ufrj.br/~coloquiomea/

Todos são muito bem vindos. Agradecemos também pela divulgação em sua
instituição.

Atenciosamente,

o comitê organizador:  Augusto Q. Teixeira (IMPA), Evaldo M.F. Curado (CBPF),
Fábio D. A. Aarão Reis (UFF),  Maria Eulalia Vares (UFRJ), Mariane Branco
Alves (UFRJ), Patrícia Gonçalves (PUC-Rio)

Resumos das palestras:

About some stochastic models on collective behaviour
Patrick Cattiaux (Univ. Toulouse)

Several mathematical models for describing the collective behaviour of
biological populations (cells, birds, ants ...) have been introduced more or
less recently. In 1970 and 1971, Evelyn F. Keller and Lee A. Segel proposed
two connected models for the chemotactic interaction of amoebae as mediated by
acrasin: a macroscopic model describing the behaviour of the local density of
cells, concentration of the chemo-attractant etc ... in terms of a system of
coupled PDE's, a microscopic one describing the microscopic (individual)
behaviour of each cell interacting with the other ones in terms of a random
system. In particular the Keller-Segel model describes the possible
aggregation of cells depending on the parameters of the system. The
macroscopic model has been extensively studied since this time, furnishing
many difficult and interesting mathematical problems, and actually the
situation is only well understood in two dimensions. The microscopic model has
been much less studied. We shall discuss another stochastic microscopic model
directly related to the macroscopic one. It is some kind of Mc-Kean Vlasov
interacting diffusions model, but with a singular attractive potential (with
the opposite sign as in the Dyson Brownian motion introduced in random matrix
theory). We shall see how the system feels the critical parameter yielding
aggregation. If we have some time, we shall also introduce a stochastic
version of the Cucker-Smale model of flocking. Here randomness is introduced
to take into account some degree of freedom of each individual, but furnishes
a negative answer to flocking.
The most common property of these two (as well as others) models is that their
properties are almost completely unknown.

Disorder relevance for pinning of random surfaces
Hubert Lacoin (IMPA)

(joint work with G. Giacomin)
Disorder relevance is an important question in Statistical Mechanics. It can
be formulated as follows: "If the Hamiltonian of model is modified by adding a
small random perturbation, does it conserve a phase transition with the same
characteristics as that of the pure model." A mathematical investigation of
this matter is of course possible only for models for which the phase
transition is rigorously understood in the pure setup, and our work concerns a
very simple and tractable model of surfaces in interaction with a defect plane.
The surfaces is modeled by the graph of a Gaussian-Free-Field $\mathbb Z^d$,
$d\ge 2$, and the interaction is given by an energy reward for each point of
the graph whose height is in the interval $[-1,1]$. The system undergoes a
wetting transition from a localized phase to a delocalized one, when the mean
energy of interaction varies.
We investigate the modification of the free-energy curve induced by the
introduction of "inhomogeneity" in the interaction. We show that in a certain
sense the critical point is left invariant by the presence of homogeneity, but
that the localization transition becomes much smoother.

--
Maria Eulalia Vares
Departamento de Métodos Estatísticos
Instituto de Matemática - UFRJ
http://www.im.ufrj.br/~eulalia