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Subgraph statistics (Benny Sudakov, ETH Zurich)

February 12 @ 12:15 pm - 1:10 pm

Given integers $k,l$  and a graph $G$, how large can be the fraction of $k$-vertex subsets of $G$ which span exactly $l$ edges?  The systematic study of this very natural  question  was recently initiated by Alon, Hefetz, Krivelevich and Tyomkyn who also proposed several interesting conjectures on this topic.

In this talk we discuss a theorem which proves one of their conjectures and implies an asymptotic version of another.  We also make some first steps towards analogous question for hypergraphs. Our proofs involve some Ramsey-type arguments, and a number of different probabilistic tools, such as polynomial anticoncentration inequalities and  hypercontractivity.

Joint work with M. Kwan and T. Tran.

Details

Date:
February 12
Time:
12:15 pm - 1:10 pm
Event Category:

Other

Speaker Name
Benny Sudakov (ETH Zurich)

Venue

Millikan 2099, Pomona College
610 N. College Ave.
Claremont, CA 91711 United States
+ Google Map

Details

Date:
February 12
Time:
12:15 pm - 1:10 pm
Event Category:

Other

Speaker Name
Benny Sudakov (ETH Zurich)

Venue

Millikan 2099, Pomona College
610 N. College Ave.
Claremont, CA 91711 United States
+ Google Map