## 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, May 19, 2016, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Asaf Ferber (Yale University)

## Iterated Log Law for various graph parameters

We show that a version of the classical Iterated Log Law of Khinchin, and independently of Kolmogorov from the 1920's, holds for various parameters in the binomial random graph model G(n,p) and in a random 0/1 Bernoulli matrices. In particular, for a constant p, we show that such a law holds for the number of copies of a fixed graph H in G(n,p), we show a similar statement for the number of Hamilton cycles in a random k-uniform hypergraph, provided that k\geq 4. In the graph case (that is, k=2), since the number of Hamilton cycles in G(n,p), denoted by X_n, does not converge to a normal distribution but rather tends to a log-normal distribution (as has been first proved by Janson), we show that a version of the Iterated Log Law holds for \log X_n. Similarly, we show that an Iterated Log Law holds for log of the permanent of a Bernoulli 0/1 matrix. No prior knowledge is required. Joint with Daniel Motealegre and Van Vu.

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