[ABE-L] Seminários PIPGEs UFSCar/USP

[Michel H. Montoril]

Caros,

Gostaríamos de convidar a todos para o próximo seminário conjunto
UFSCar/ICMC-USP, que ocorrerá no dia *16/09*, *às 14h*. Seguem informações
abaixo.

Saudações,
Michel

*Scheduled for:*
Sep 16, 2022, at 2:00 pm
(GMT-03:00) Brasilia Standard Time - Sao Paulo

*Video call link HERE <https://meet.google.com/jfs-kcbs-fkw>.*

*Speaker:*
Jean-René Chazottes (Ecole Polytechnique, France)

*Title:*
Quasi-stationary distributions, extinction and resilience in ecological
models

*Abstract:*
We consider birth-and-death processes going eventually to extinction with
probability one, accounting for the finiteness of resources. A classical
result says that if we rescale such a process by a parameter K and fix a
finite horizon time, then the resulting sample paths are very close to the
solutions of a differentiable equation (deterministic dynamical system)
with high probability, when K goes to infinity. The corresponding vector
field is given by the difference between the birth and death rates. In
particular, the limit when times goes to infinity does not commute with the
limit when K goes to infinity.
In this talk, I will try to explain what can be said for finite times and
for finite K. A central object is the so-called quasi-stationary
distribution which plays the role of a stationary distribution when
conditioning upon non-extinction. Another one is the mean-time to
extinction. Finally, I will touch upon the following question. Observing a
realization of the process, can we determine the so-called engineering
resilience? This quantity can be defined as the reciprocal of the
characteristic return time to, say, a fixed point after a (small)
perturbation.To answer this question, we establish two relations which
intermingle the resilience, which is a macroscopic quantity defined for the
dynamical system, and the fluctuations of the process, which are
microscopic quantities.


*Bio:*
Jean-René is a Senior Researcher at CNRS at Ecole Polytechnique in France.
His main research interests are in probabilistic properties of dynamical
systems (limit theorems and concentration inequalities), statistical
physics, and mathematical ecology. He defended his PhD thesis in 1999 in
mathematical physics in Marseille. Before joining CNRS, he did a postdoc in
Mexico and then at IME in São Paulo. He is also the director of the Centre
de Physique Théorique of Ecole Polytechnique.

===============================
/* Michel H. Montoril,
 * Assistant Professor,
 * Department of Statistics,
 * Federal University of São Carlos,
 * São Carlos, SP, 13565-905, Brazil
 */
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