Brownian Polymers in Poissonian Environment: a survey

We consider a space-time continuous directed polymer in random environment. The path is Brownian and the medium is Poissonian. We review many results obtained in the last decade, and also we present new ones. In this fundamental setup, we can make use of fine formulas and strong tools from stochastic analysis for Gaussian or Poisson measure, together with martingale techniques. These notes cover the matter of a course presented during the Jean-Morlet chair 2017 of CIRM "Random Structures in Statistical Mechanics and Mathematical Physics" in Marseille.Comment: 64 pages. 4 figure

Cristina Trivulzio Belgiojoso y su idea de estado: una patriota politóloga

Resumen:Cristina Trivulzio Belgiojoso es una patriota italiana del siglo XIX. Escritora, periodista, y activista, participa activamente en movimiento que lleva a la unificación italiana en el 1861. En su ensayo, describe su sueño de una nación más fuerte, justa, culta y solidaria. En un periodo de plena éxtasis celebrativa y patriótica, ella supo analizar lucidamente los defectos de la nueva Italia.</jats:p

Hausdorff Dimension of the Record Set of a Fractional Brownian Motion

We prove that the Hausdorff dimension of the record set of a fractional Brownian motion with Hurst parameter $H$ equals $H$