[EstudiantesMatemática] charlas la semana que viene

[Paola Bermolen]

Hola a todos,

Les escribo porque la semana que viene nos van a estar visitando dos profesores Matthieu Jonckheere (UBA) y Mathieu Feuillet (INRIA).
Por tanto habrán varias charlas que pueden resultar de interés para ustedes.
Por cualquier consulta, estoy a las órdenes.

Saludos
Paola


LUNES 5 DICIEMBRE 11:30hs: SEMINARIO PROBABILIDAD Y ESTADÍSTICA - CMAT/FAC. CIENCIAS (en español)

Título: The Fleming Viot process driven by subcritical branching: a selection principle. 
Prof. Matthieu Jonckheere.  Joint work with A. Asselah, P. Groisman, P. Ferrari.


Resumen: 
We consider Fleming Viot processes having the following dynamics: N particles move independently according to the dynamics of a subcritical branching process until 
they hit 0, at which point, they instantaneously and uniformly choose the

position of one of the other particles.


We first establish a coupling between the FV processes (associated to any one-dimensional dynamics) and multitype branching processes.

This allows us to prove convergence of scaled version of the \fv processes and ergodicity for fixed N.

Using large deviations estimate for subcritical branching processes, this coupling further allows to obtain useful drift inequalities for the maximum of

the Fleming Viot process.These inequalities imply in turn tightness of the family of empirical measures under

the stationary measure of the FV process. Finally, we prove a selection principle: the empirical measures converge to the extremal quasi-stationary

measure of the branching process when N tends to infinity.


 
MARTES 6 DE DICIEMBRE 11:30hs: FACULTAD DE INGENIERÍA - SALÓN A CONFIRMAR.

Título:  Scaling methods for stochastic networks.
Prof. Mathieu Feuillet. This presentation is partly based on joint works with (alphabetically)
 Th Bonald, A Proutiere, Ph. Robert.

Resumen:
It is usually quite difficult to study the behavior of a
multi-dimensional Markov process describing the evolution of a
stochastic network.
When it exists, the equilibrium distribution of stochastic networks is
 not known apart from some specific classes of processes. Moreover,
 even when this distribution is known, the dynamics of interest may not
 be the equilibrium. Some insight into the behavior of these networks
 can nevertheless be obtained through limit procedures which can be
 roughly described as follows: for some system parameter N, with an
 appropriate scaling, when N tends to infinity, the evolution of the
 state of the network converges to a much simpler process.
 After an introduction to some classical scaling methods, we give
 several illustrative examples and emphasize the difficulties due to
 border effects. We explain some techniques used to deal with these
 difficulties including notably Skorokhod problems and stochastic
 averaging.


JUEVES 8 DE DICIEMBRE 11:30hs: FACULTAD DE INGENIERÍA - SALÓN A CONFIRMAR.

Título: Martingale methods for computing hitting times in the
Ehrenfest and Engset models.
Prof. Mathieu Feuillet.  Joint work with Philippe Robert.

 Resumen:
Martingale methods are a powerful tool to investigate the transient
 behavior of certain stochastic systems. For instance, many results on
 random walks and Brownian motion have been obtained thanks to
 exponential martingales. In this talk, we consider two classical
 stochastic processes, the Ehrenfest process, introduced in 1907 in the
 kinetic theory of gases to describe the heat exchange between two
 bodies and the Engset process, one of the early (1918) stochastic
 models of communication networks. We explain how to obtain a certain
 familiy of simple non-negative martingales and we derivate the Laplace
 transform of hitting times for both models. Finally, using standard
 analysis tools, we investigate the asymptotic behavior of the
 distributions of hitting times of these two processes when the number
 of particles/sources goes to infinity.



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