Noticias en español
Computer-assisted proof of robust transitivity.
RESUMEN: A smooth dynamical system is transitive if it has a dense orbit, loosely meaning that it has some chaos in a topological sense. If this property holds for all diffeomorphisms in a C¹-neighborhood, we say that systems in this neighborhood are robustly transitive. By Bonatti, Diaz and Pujals (2003), robustly transitive diffeomorphisms are volume hyperbolic, and thus they have positive topological entropy, being chaotic in a strict sense and in a robust way. Robust properties are key in classifying smooth dynamical systems, and they are also desirable to model applications. We develop...
Read MoreThe Haagerup property.
Abstract: The Haagerup property is an analytic property of groups that generalises amenability. It originated from the study of C*-algebras, and it has found applications in several areas of mathematics, including harmonic analysis, geometric group theory, topology, and ergodic theory. This talk will consist in an introduction to this property and its connections to group actions on Banach spaces.
Read MorePoisson representation of Brownian bridge.
Resumen: We consider Brownian motion $(B(t))$, for $t\in[0,1]$, and Brownian bridge $BB(t)$, the Brownian motion conditioned to return to $0$ at time~$1$. The following identity is well known,(1)\,\hfill law of $(BB(t))_{t\in[0,1]}= $ law of $(B(t)- tB(1))_{t\in[0,1]}$. \hfill\ A centered and rescaled Poisson point process $B^\varepsilon(t)$ converges to Brownian motion, where $\varepsilon$ is the scaling parameter going to $0$. For each $\varepsilon>0$, we construct a coupling $(B^\varepsilon(t),BB^\varepsilon (t))$ satisfying an almost sure version of (1). Taking $\varepsilon\to0$...
Read MoreProphet Inequalities with Moment Knowledge.
Abstract: In this talk, we study a variant of the prophet inequality with limited information, where the decision maker only has access to the first k moments of each random variable, rather than their full distributions. Our main result is that, for any k, even one dependent on n, the best possible competitive ratio is Θ(1/ log(n)), which we show can already be achieved with knowledge of the first moment only. Our result implies that the moments are not very informative in this setting, so extra information is needed if one aims for better guarantees. To showcase the impact of extra...
Read MoreWell-posedness for 2D non-homogeneous incompressible fluids with general density-dependent odd viscosity
Abstract: Viscosity in fluids is often related to the dissipation of energy. However, in physical systems where the microscopic dynamics do not obey time-reversal symmetry, a non-dissipative viscosity can emerge, often referred to as “odd viscosity”. In this talk, we will consider the initial value problem for a system of equations describing the motion of two-dimensional non homogeneous incompressible fluids exhibiting odd viscosity effects. We will prove the local existence and uniqueness of strong solutions in sufficiently regular Sobolev spaces. Differently from previous...
Read MoreDomination criterion for some positive operators and quasi-stationary distributions.
Resumen: After a short introduction to the concept of quasi-stationary distributions, I will present the typical and well known “finite state space” convergence results. In a second time, I will present domination criteria for the quasi-compactness of positive operators and show some applications of these spectral theoretical results for the study of quasi-stationary distributions. The talk will conclude with an illustration on the interplay between these results and recent ones on weighted branching processes, obtained in collaboration with Nicolas Zalduendo.
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