# Brownian motion and beyond: first-passage, power spectrum, non-Gaussianity, and anomalous diffusion

## TL;DR

This paper reviews recent advances in the study of Brownian motion, emphasizing new experimental techniques like superresolution microscopy and their impact on understanding stochastic processes, including first-passage, power spectrum, non-Gaussianity, and anomalous diffusion.

## Contribution

It provides a comprehensive summary of recent experimental and theoretical developments in Brownian motion and stochastic processes driven by novel experimental methods.

## Key findings

- Advances in superresolution microscopy have enhanced understanding of Brownian motion.
- Recent theoretical frameworks address non-Gaussianity and anomalous diffusion.
- Experimental findings reveal new aspects of stochastic processes in various disciplines.

## Abstract

Brownian motion is a ubiquitous physical phenomenon across the sciences. After its discovery by Brown and intensive study since the first half of the 20th century, many different aspects of Brownian motion and stochastic processes in general have been addressed in Statistical Physics. In particular, there now exist a very large range of applications of stochastic processes in various disciplines. Here, we highlight some of the advances in stochastic processes prompted by novel experimental methods such as superresolution microscopy. Here we provide a summary of some of the recent developments highlighting both the experimental findings and theoretical frameworks.