Programa

 

Miércoles Jueves Viernes
10:00-11:15 Powell Hilario Powell
11:15-11:45 Café Café Café
11:45-13:00 Hilario Powell Hilario
13:00-15:00 Almuerzo Almuerzo Almuerzo
15:00-16:00 Bertin Olivero Méleard
16:00-16:30 Café Café Café
16:30-17:30 Cabezas González
Cena

Mini-Cursos:

Marcelo Hilario, Universidade Federal de Minas Gerais

Multiscale methods for random walks in dynamic random environments

Ellen Powell , University of Durham (Notes)

Introduction to the Gaussian free field

Charlas invitadas:

Karine Bertin , Universidad de Valparaíso

Estimación adaptativa en modelos de densidad y regresión funcional

En esta charla, presentaremos métodos de estimación para estimar funciones no-paramétricas en modelos de densidad y en modelo de regresión funcional asociado a proceso de Wiener. En el modelo clásico de la densidad estudiaremos las propiedades de estimadores de tipo núcleo asumiendo que las funciones a estimar pertenecen a clases de funciones de Holder. Presentaremos el método de Goldenshluger-Lepski (2011) que permite obtener estimadores que se adaptan a la regularidad de la función. Mostraremos cómo extender este método en el caso de la regresión funcional donde la variable regresora es un proceso de Wiener.

Manuel Cabezas , Pontificia Universidad de Chile

Historical lattice trees

Héctor Olivero, Universidad de Valparaíso

A paracontrolled approach for the Brox diffusion

Manuel González , Universidad del Bío Bío

Two basic models from statistical physics.

In this talk I will speak about an Ising model with an alternated external field. The aim is to show some tools used to characterize the low-temperature phase diagram.
In addition, I will introduce a family of random walks with memory, which is inspired by the so-called elephant random walk. I will focus on the asymptotic behaviour of the position of the walker.
Sylvie Méleard , École Polytechnique

Multiscale eco-evolutionary models: from individuals to populations

Motivated by recent biological experiments, we emphasize the effects of
small and random populations on long time population dynamics. We will
quantify such effects on macroscopic approximations. The individual behaviors
are described by the mean of a stochastic measure-valued process. We
study different long time asymptotic behaviors depending on the assumptions
on mutation size and frequency and on horizontal transmission rate. In some
cases, simulations indicate that these models should exhibit surprising asymptotic
behaviors such as cyclic behaviors. We explore these behaviors on a
simple model where population and time sizes are on a log-scale. Explicit criteria
are given to characterize the possible asymptotic behaviors.