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401-3604-66L  Special Topics in Probability

SemesterHerbstsemester 2016
DozierendeP. Nolin
Periodizitäteinmalige Veranstaltung
LehrspracheEnglisch


KurzbeschreibungThe goal of this course is to present recent developments in Percolation Theory
LernzielThe goal of this course is to present recent developments in Percolation Theory
InhaltIndependent percolation is obtained by deleting randomly (and independently) the edges of a lattice, each with a given probability p between 0 and 1. One is then interested in the connectivity properties of the random subgraph so-obtained. It is arguably the simplest model from statistical mechanics that displays a phase transition, a drastic change of behavior as the parameter p varies.

We will first present classical tools and properties of percolation theory: in particular correlation inequalities, exponential decay of connection probabilities, and uniqueness of the infinite connected component. We will then discuss recent developments: for example percolation on Cayley graphs, and continuum limits in two dimensions.
LiteraturB. Bollobas, O. Riordan: Percolation, CUP 2006
G. Grimmett: Percolation 2ed, Springer 1999
Voraussetzungen / BesonderesPrerequisites:
401-2604-00L Probability and Statistics (mandatory)
401-3601-00L Probability Theory (recommended)