Fri, 09.02.2018, 15:15 |
I. Pinning model, universality and rough paths II. Coexistence of competing first-passage percolation on hyperbolic graphs.Rhein-Main-KolloquiumSpeaker:
Prof. Francesco Caravenna / Dr. Elisabetta CandelleroHost:
AG StochastikRoom:
S2 | 07 Raum 167I. One of the simplest, yet challenging exampes of "disordered systems" in statistical mechanics is the so-called pinning model. This can be roughly described as a random walk which interacts with a random medium (the "disorder") concentrated along a line. In a suitable weak-disorder regime, this model admits a continuum scaling limit, which can be characterized through the solution of a singular stochastic equation, driven by a Brownian motion. In this talk, we present a robust analysis of this equation, using ideas from rough paths. This sheds light on the effect of disorder and leads naturally to universality results. II. We consider two first-passage percolation processes FPP_1
and FPP_{\lambda}, spreading with rates 1 and \lambda > 0
respectively, on a non-amenable hyperbolic graph G with bounded degree. |
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Fachbereich Mathematik

Technische Universität Darmstadt

Schlossgartenstraße 7

64289 Darmstadt