Мини-курс "Strong probability distances and limit theorems", проф. Сергей Бобков (Университет Миннесоты, ВШЭ)

On May 17, 24 Sergey Bobkov (University of Minnesota, Higher School of Economics) will give a mini-course   "Strong probability distances and limit theorems".

Address: HSE Faculty of Computer Science, Kochnovsky proezd, 3 (room 205)
Language of instruction: English

Schedule: 

Lectures explore strong distances in the space of probability distributions, including total variation, relative entropy, chi-squared and more general Renyi/Tsallis informational divergences, as well as relative Fisher information. Special attention is given to the distances from the normal law. The first part of the course is devoted to the general theory and the second part to the behavior of such informational distances along convolutions and associated central limit theorem.

Lectures 1-2. General theory of Renyi and Tsallis informational divergences. Relative entropy and chi-squared distance as particular cases. Relationship with total variation. Pinsker-type inequalities.
Lectures 3-4. Entropy power inequality. Basic properties of relative entropy. Fisher information. Stam’s inequality and its applications. 
Lectures 5-6. Informational divergences from the normal law. Poincare and logarithmic Sobolev inequalities. Cramer’s exponential series and their applications to the chi-squared distance. Superadditivity with respect to dimension. 
Lectures 7-8. Local limit theorem (the central limit theorem for densities) and Edgeworth expansions. Convergence to the normal law in Renyi’s distances. 

For the pass to the building contact Vlada Kuznetsova (vkuznecova@hse.ru).