Seminar Interacting Random Systems
- Mittwoch, 30.10.2019, 11:30 Uhr (WIAS-406)
Dr. Niccolo Torri, Université Paris Nanterre, Frankreich:
Directed polymer in a heavy-tail random environment
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
A classical problem in the field of disordered systems is to understand the behaviour of a directed polymer in interaction with a random environment. Mathematically, the directed polymer is modeled by a directed random walk and the random environment is a sequence of random variables which can interact with the random walk perturbing its behaviour, giving rise to super-diffusive transversal fluctuations and localisation phenomena. Understanding the typical trajectories of the the walk is a very challenging issue and several results have been obtained when the random environment has exponential moments. In this talk we consider the case of a heavy-tail random environment, that is, the environment?s distribution function decades polynomially with exponent $alpha >0$. We mainly focus on the case in which the random environment has no second moment ($alphain (0,2)$), finding the super-diffusive transversal fluctuations of the polymer as function of the parameter $alpha$. Joint work with Quentin Berger (Sorbonne Université).
Seminar Interacting Random Suystems