Andrei Kupavskii - On the second degrees of vertices in the Buckley--Osthus random graph model

This talk is devoted to Buckley-Osthus random graph model. It is known that the degree distribution in this random graph model obeys power law. We will show that the distribution of second degrees also obeys power law. The proof of this fact consists of two parts. First is the calculation of the expectation of the number of vertices of second degree k. Second one is the proof of the concentration around the expectation. We will focus on the second part. The proof of the concentration is a nontrivial application of Talagrand inequality.