# Category Archives: Random graphs

## Guest post by Miklos Racz: Entropic central limit theorems and a proof of the fundamental limits of dimension estimation

In this post we give a proof of the fundamental limits of dimension estimation in random geometric graphs, based on the recent work of Bubeck and Ganguly. We refer the reader to the previous post for a detailed introduction; here … Continue reading

## Guest post by Miklos Racz: Estimating the dimension of a random geometric graph on a high-dimensional sphere

Following the previous post in which we studied community detection, in this post we study the fundamental limits of inferring geometric structure in networks. Many networks coming from physical considerations naturally have an underlying geometry, such as the network of … Continue reading

## Guest post by Miklos Racz: A primer on exact recovery in the general stochastic block model

Foreword: this will be a series of blog posts written by our Theory Group postdoc Miklos Racz. It is essentially the transcript of a mini-course that Miki gave at the University of Washington and at the XX Brazilian School of … Continue reading

## Some pictures in geometric probability

As I discussed in a previous blog post, I have been recently interested in models of randomly growing networks. As a starting point I focused my attention on the preferential attachment rule and its variants, in part because its ubiquity … Continue reading

## What’s the (hi)story of my network?

First an announcement: we have researcher and postdoc positions available in Theory Group at MSR, and I may have a position for an intern in the summer. If you are a talented young mathematician with interests in the kind of … Continue reading

## On the influence of the seed graph in the preferential attachment model

The preferential attachment model, introduced in 1992 by Mahmoud and popularized in 1999 by Barabási and Albert, has attracted a lot of attention in the last decade. In its simplest form it describes the evolution of a random tree. Formally we denote by … Continue reading

## Random-Approx 2013

Last week I attended the Random-Approx conference at Berkeley. I missed quite a few talks as I was also settling in my new office for the semester at the Simons Institute so I will just report on the three invited talks: Luca Trevisan gave a … Continue reading

## Guest post by Philippe Rigollet: Estimating structured graphs

Last wednesday, Sourav Chatterjee was speaking in the Mathematics Colloquium here at Princeton. While he is most famous for his contributions to probability, especially using Stein’s method, this talk was rather statistical. The problem was interesting and its solution simple enough that … Continue reading

## Proof of the lower bound

Our proof of the lower bound for the clique number of random geometric graphs (see Theorem 1 in the previous post) is a little bit contrived, but it might actually have some value. Our approach can be described as follows. … Continue reading

## Clique number of random geometric graphs in high dimension

I would like to discuss now another class of random graphs, called random geometric graphs. In general a random geometric graph arises by taking i.i.d. random variables in some metric space, and then putting an edge between two of these random … Continue reading