Probability and Stochastic Analysis - University of Bonn
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Graduate Seminar Probability Theory S4F1, SS 2013

Self-avoiding walks and non-Markovian random structures

Time and Place:  Thursdays, 14-16h, 0.006, Mathematics Center

Preparatory meeting: Wednesday, February 6, 16h, in room 3.037  

                         

Those interested in participating (in particularly those who cannot come on the 6th), please send me an email!!!


Topic:

The classical non-Markovian random geometric structure is the self-avoiding random walk. As simple as it is to describe, analysing its large-scale properties is a highly non-trivial problem. Methods (lace expansion) have been devised to deal with it in high enough dimensions, where the constraint of self-avoidance becomes irrelevant, and recently methods from conformal analysis have been used to tackle the two-dimensional case. In this seminar we pick up some of these developments. The basic text will be the Clay lectures notes by Bauerschmidt et al. There are a number of further notes and papers by Gordon Slade (lace expansions) and Duminil-Copin and Smirnov. They use Smirnov's approach of discrete complex analysis, which is quite a fascinating topic in itself. Depending on the participants interest, we could also go into this topic more deeply.


Further reading:

Prelinimary schedule: