# Variations and extensions of the Gaussian concentration inequality, Part I

## TL;DR

This paper extends the Gaussian concentration inequality to settings beyond Lipschitz and Gaussian assumptions, providing a more direct theoretical approach and applying it to heavy-tailed random variables.

## Contribution

It introduces variations and extensions of the classical Gaussian concentration inequality that do not rely on Lipschitz or Gaussian assumptions, offering a more straightforward theoretical framework.

## Key findings

- Extended concentration inequalities for non-Lipschitz functions
- Application to linear combinations of heavy-tailed variables
- More direct theoretical approach

## 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.