Variations and extensions of the Gaussian concentration inequality, Part I

Abstract

The classical Gaussian concentration inequality for Lipschitz functions is adapted to a setting where the classical assumptions (i.e. Lipschitz and Gaussian) are not met. The theory is more direct than much of the existing theory designed to handle related generalizations. An application is presented to linear combinations of heavy tailed random variables.

Mathematics Subject Classification (2020):

• 60E05
• 60E15
• 52A27
• 52A30

Key words:

• Gaussian concentration inequality
• heavy tailed random variables