This week, we will discuss Section 1.6 and 1.7 of the lecture notes of Wu and Polyanski: 
http://people.lids.mit.edu/yp/homepage/papers.html

Working Group in Information Theory is a self-educational project in the department. Techniques based on information theory have become essential in high-dimensional probability, theoretical computer science and statistical learning theory. On the other hand, information theory is not taught systematically. The goal of this group is to close this gap.

Working Group in Information Theory is a new self-educational project in the department. Techniques based on information theory have become essential in high-dimensional probability, theoretical computer science and statistical learning theory. On the other hand, information theory is not taught systematically. The goal of this group is to close this gap. We will meet weekly and take turns to present the materital from the lecture notes of Wu and Polyanski: 

http://people.lids.mit.edu/yp/homepage/papers.html

Everyone, including especially graduate students, is welcome to participate!

I will start presenting Section 1.

We will keep going over Tikhomirov’s argument on the asymptotic singularity of random Bernoulli matrices, found here: https://arxiv.org/pdf/1812.09016.pdf

We prove the “net theorem” discussed in my previous talk in the Probability seminar. The “lite version” of the theorem states the existence of a net around the sphere of cardinality 100^n, such that for every random matrix A with independent columns, with probability 1-5^{-n}, the values of |Ax| on the sphere can be compared to its values on the net. The error in this comparison is optimal, and the formulation of the theorem is scale-invariant. We emphasize that the only assumption required for this is the independence of columns. The proof consists of four steps, and shall be outlined.

We will discuss the paper by Sebastien Bubeck and Ronen Eldan with that title. 
The paper can be found here (https://arxiv.org/abs/1507.06580).