### Lower Deviations and Convexity

- Series
- Stochastics Seminar
- Time
- Thursday, February 27, 2020 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Petros Valettas – University of Missouri, Columbia

While deviation estimates above the mean is a very well studied subject in high-dimensional probability, for their lower analogues far less are known. However, it has been observed, in several key situations, that lower deviation inequalities exhibit very different and stronger behavior. In this talk I will discuss how convexity can serve as a key feature to (a) explain this distinction, (b) obtain improved lower tail bounds, and (c) characterize the tightness of Gaussian concentration.