## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, October 01, 2009, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Thomas Rast

## Positive and negative correlation

On the positive correlation side, we discuss the FKG Theorem (Fortuin, Kasteleyn and Ginibre, 1971): under the (frequently easy to check) _positive lattice condition_, the seemingly much stronger _positive association property_ $E[fg] \le E[f]E[g]$ follows. We also give a proof outline based on a simplified version. On the negative correlation side, not nearly as much is known. We look at the example of uniform spanning trees, where negative correlation and in fact negative association is known to hold. Based on a survey of Pemantle (1999), we then give a brief overview of possible generalisations.

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