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Gaussian convexity

Introductory Workshop: phenomena in high dimensions August 21, 2017 - August 25, 2017

August 22, 2017 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Ramon Van Handel (Princeton University)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Dimension-free phenomena

  • geometry of Gaussian measures

  • rearrangements

  • Brunn-Minkowski inequalities

  • Ehrhard inequality

  • concentration of measure

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

5-VanHandel

Abstract

It has long been known that Gaussian measures possess unique convexity properties within the class of log-concave measures. In particular, a remarkable sharp form of Gaussian convexity was discovered by A. Ehrhard in the early 1980s, but has mostly remained somewhat of a beautiful curiosity. In recent work, however, this inequality, the theory surrounding it, and its utility in applications have become significantly better understood. My aim in these talks is to review and discuss in some detail several recent developments surrounding this theory and its applications to Gaussian concentration phenomena (by us as well as by other authors). I will also highlight some key mysteries that remain.

Supplements No Notes/Supplements Uploaded
Video/Audio Files

5-VanHandel

H.264 Video 5-VanHandel.mp4 397 MB video/mp4 rtsp://videos.msri.org/data/000/029/248/original/5-VanHandel.mp4 Download
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