Noticias en español
Scaling limits of individual-based models in adaptive dynamics allowing for local extinction or survival of population.
Abstract: Starting from an individual-based birth-death-mutation-selection model of adaptive dynamics with three scaling parameters (population size, mutation rate, mutation steps size), we will describe several scaling limits that can be applied to this model to obtain macroscopic models of different natures (PDE, stochastic adaptive walks), which allow to characterize long-term evolution of the population. Motivated by biological criticisms on the time-scale of evolution and the absence of local extinctions in the obtained macroscopic models, we propose a new parameter scalings under which...
Read MoreEstimación Adaptativa en Modelos de Regresión Funcional Asociado a Proceso de Wiener.
Resumen: En esta charla, estudiaremos métodos de suavizamiento para estimar funciones no-paramétricas. Veremos cómo elegir los parámetros de suavizamiento con el objetivo de tener estimadores óptimos. Más específicamente, introduciremos 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. Definiremos una familia de estimadores para la función de regresión basándose en la descomposición de Wiener...
Read MoreExistence of quasi-stationary distributions for downward skip-free Markov chains.
Abstract: I talk about existence of a quasi-stationary distribution for downward skip-free continuous-time Markov chains on non-negative integers stopped at zero. The scale function for these processes is introduced and the boundary is classified by a certain integrability condition on the scale function, which gives an extension of Feller’s classification of the boundary for birth-and-death processes.The existence and the set of quasi-stationary distributions are characterized by the scale function and the new classification of the boundary.
Read MoreDistance evolutions in growing preferential attachment graphs.
Abstract: In this talk we will study the evolution of the graph distance between two fixed vertices in dynamically growing random graph models. More precisely, we consider preferential attachment models with parameters such that the asymptotic degree distribution has infinite second moment. First, we grow the graph until it contains $t$ vertices, then we sample $u_t, v_t$ uniformly at random from the largest component and study the evolution of the graph distance as the surrounding graph grows. This yields a stochastic process in $t’\ge t$ that we call the distance evolution. We...
Read MoreA limit law for the most favorite point of a simple random walk on a regular tree.
We consider a continuous-time random walk on a regular tree of finite depth and study its favorite points among the leaf vertices. We prove that, for the walk started from a leaf vertex and stopped upon hitting the root, as the depth of the tree tends to infinity the maximal time spent at any leaf converges, under suitable scaling and centering, to a randomly-shifted Gumbel law. The random shift is characterized using a derivative-martingale-like object associated with the square-root local-time process on the tree.
Read MoreOn some interacting particle systems related to random matrices.
Abstract: The talk is about two types of interacting particle systems related to the classical ensembles of random matrices. The prototypical examples are Dyson Brownian motion (also called non-intersecting Brownian motions) and Brownian TASEP (also called Brownian motions with one-sided collisions/reflections) respectively. I will discuss explicit formulae for their distributions, their correlation functions and some non-trivial connections between the two types of interacting particle systems. The bulk of the talk will be mainly focussed on surveying results for the Gaussian/Brownian...
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