Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, June 09, 2015, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Jan Hazla

Same-set expansion on correlated probability spaces

I will present a solution to the following problem:

Let S := {0, 1, 2}^n and let A be a subset of S such that |A| / |S| = mu. Sample a random vector X = (X_1, ..., X_n) uniformly from S. Sample another random vector Y = (Y_1, ..., Y_n) such that for each coordinate i independently Y_i is uniform in { X_i, X_i+1 (mod 3) }.

Show that Pr[ X in A and Y in A] >= f(mu) > 0, i.e., a lower bound that is independent of n.

I will explain the context of the problem and outline techniques needed to solve it.

Joint work with Thomas Holenstein and Elchanan Mossel.


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