Professur Stochastik

 

Seminar on Large Deviations and Concentration inequalities

organised by Francisco Hoecker-Escuti and Ivan Veselić.

In the seminar we will discuss various types of estimates on probabilities associated to a large number of trials or experiments. The trials are often times, but not always, assumed to be independent and/or identically distributed. In many cases the probabilistic estimates are very efficient in the sense that they converge to zero exponentially fast in the number of trials. Such types of estimates are called, depending on the scientific context and the specific form, Large Deviations Principles or Concentration inequalities, respectively. They have a wide range of applications in analysis, statistics, mathematical physics, combinatorics, machine learning theory etc.

Prerequisites:

Participants should have a good knowledge of probability theory, certified for instance by an exam in the course B 10 Stochastik and possibly by futher courses in probability theory.

Samples of possible talks/topis for partcipating students:

  • The Sections 2.1, 2.2. and 2.3 in the Book of A. Dembo und O. Zeitouni could form each a separate topic for a talk. The whole chapter devoted to the Large DeviationsPrinciple for finite alphabets can be downloaded here
  • The Section 4 in Chapter I, dealing with the range of a random walk, in the Book of F. Spitzer is a topic for a talk.

Venue and time:

  • The first meeting will be on Thursday 18. October at 13.45 , when we will decide about the further dates of the seminar according to the availability of the participants.
  • We have reserved the seminar room: Rh-Str 41/705 for the seminar.
  • If you are a student interested in the seminar feel free to send me an email enquiring about the seminar.

Literature

Schedule

border="8" cellspacing="10" cellpadding="20"
Date Time and comments Title Speaker
1. November 13:45 Large deviations and concentration inequalities Francisco Hoecker
8. November 13:45 The Hoeffding inequality and the Effron-Stein inequality Francisco Hoecker
15. November 14:00 Glivenko--Cantelli theorems and the IDS (I) Ivan Veselić
22. November 13:45 Glivenko--Cantelli theorems and the IDS (II) Christoph Schumacher
28. November 15:30 (jointly with the Forschungsseminar) Concentration of mass and central limit property for isotropic convex bodies in high dimensions Jürgen Voigt
4. December 17:15 Rate function for k-Tuples Hartmut Leister
13. December 13:45 Approximations of the IDS on Sofic groups Christoph Schumacher
Christmas holydays Christmas holydays Christmas holydays Christmas holydays
10. January 13:45 Concentration for Lipschitz function, Dudley's integral inequality, Kolmogorov's chaining Francisco Hoecker
17. January 13:45 Berry-Esseen proof of Tao and Vu, Lindeberg's proof of CLT Francisco Hoecker
22. January 17:15 Lifschitz Tails via linear coupling Peter Stollmann
31. January 13:45 Towards a proof of Lifschitz Tails on polynomially growing graphs Reza Samvhat
4. February 13:45 Proof of DeHardt's Theorem Christoph Schumacher