Itai Ben Yaacov : Independence and mean widths

Posted by , part of the Logic Seminar.

At

Feb. 11, 2008, 4 p.m.

In

SEO 427

Abstract

A relation between two sets X and Y is said to be dependent if it does not shatter arbitrarily large finite subsets of X. Similarly, a function X x Y -> [0,1] is dependent if for every e > 0 it does not e-shatter arbitrarily large finite subsets of X. A characterisation of dependent functions in terms of the growth rate of the mean width of a family of associated convex compacts is essential to proving that the expectation of a random family of uniformly dependent functions is again dependent. Model theoretically, this means that the Keisler randomisation of a dependent theory is again dependent, answering a question of Pillay and allowing a more direct approach to the study of Keisler measure in (classical) dependent theories.

there shall be tea at 4pm, talk at 4:20. Some of us will go out for dinner afterwards.