Measure Concentration Minischool

organized by F. Matúš

Institute of Information Theory and Automation, Prague Room 25, UTIA AVCR, Pod Vodárenskou věží 4, 18000 Praha 8

Tuesday, August 21, 2012

• 9:00-9:30 Introductory examples (F. Matus)
• 9:30-11:00 Hoeffding and Bennett inequalities [4, 6] (J. Rauh)
• 11:30-12:30 Improvements of Hoeffding inequalities (P. Harremoes)
• 14:30-15:30 Concentration functions and inequalities I [5] (S. Weis)
• 15:30-16:30 Concentration functions and inequalities II (M. Muller)
• 17:00-18:00 Matrix concentration inequalities (F. Matus)

Wednesday, August 22, 2012

• 9:00-10:00 Stein’s method for concentration inequalities [3, 1](S. Weis)
• 10:00-11:00 Talagrand inequality [4] (J. Rauh)
• 11:30-12:30 Dembo’s proof of Talagrand inequality [2] (F. Matus)
• 14:30-15:30 Log-Sobolev inequalities (P. Harremoes)
• 15:30-17:00 Concentration in quantum settings (M. Muller)

References

• [1] S. Chatterjee (2007) Stein’s method for concentration inequalities. Probab. Th. and Relat. Fields 138 305–321.
• [2] A. Dembo and O. Zeitouni (1998) Large Deviations Techniques and Applications. Springer, New York.
• [3] G. Lugosi (2006) Concentration-of-measure inequalities (on web)
• [4] C. McDiarmid (1998) Concentration. in: Probabilistic Methods for Algorithmic Discrete Mathematics M. Habib et at (Eds.) Springer, Berlin, 195–248.
• [5] M. Ledoux (2001) The Concentration of Measure Phenomenon. AMS Math. Surveys and Monographs 89.
• [6] I. Sason (2012) Refined versions of the Azuma-Hoeffding inequality with applications in information theory.