Noticimat 42

Hora: 19:15 GMT-6

Enlace de transmisión: https://cuaed-unam.zoom.us/j/96975648353  

 

Ponente 1: Isaac González 

Título: Comportamiento asintótico de momentos de una difusión de ramificación crítico en un dominio acotado y un resultado tipo Yaglom

Resumen: Tomamos un proceso de ramificación crítico en un dominio acotado en el que cada partícula se mueve de acuerdo a una difusión y cada que una de ellas toca la frontera de del domino ésta muere y es enviada a un estado cementerio. En esta plática daremos una expresión para los momentos de dicho proceso y la utilizaremos para dar un resultado sobre su comportamiento asintótico. Para finalizar, usaremos este resultado para dar una prueba de un teorema tipo Yaglom para el proceso condicionado a seguir vivo. Este es un trabajo conjunto con Andreas Kyprianou.

 

Ponente 2: Julia Palacios

Título: Cadenas de Markov locales de árboles de coalescencia

Resumen: Ranked tree shapes and ranked genealogies are binary tree structures commonly used in biological areas. These trees are used to model the ancestral history of a sample, typically a sample of DNA or RNA sequences. We will discuss two representations of ranked tree shapes as constrained matrices of integers and ordered matchings. We exploit these representations to define an ergodic Markov chain on the space of ranked tree shapes with uniform stationary distribution. We will study its mixing time and compare to other related work. This is based on joint work with Mackenzie Simper.

 

Ponente: Ivan Nourdin (University of Luxembourg)

Título: The functional Breuer-Major theorem

Hora: 10:00 GMT-6

Enlace de transmisión: Zoom (Meeting ID: 939 7440 2639; contraseña: cimat2008)

Resumen: Let X be a zero-mean stationary Gaussian sequence of random variables with covariance function p satisfying p(0)=1. Let f be a function of Hermite rank d bigger than 1. The celebrated Breuer–Major theorem asserts that, if p^d is summable then the finite dimensional distributions of the normalized sum of f(X_i) converge to those of a standard Brownian motion (up to some multiplicative constant). Surprisingly, and despite the fact this theorem has become over the years a prominent tool in a bunch of different areas, a necessary and sufficient condition implying the weak convergence in the space of càdlàg functions endowed with the Skorohod topology was still missing. We will explain in this talk how to fill this gap. This is joint work with David Nualart, based on a recent paper published in PTRF.