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

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.

19 pages, 3 figures, StatPhys27 special issue

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Cited by in corpus (20)

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• Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories
• Universal spectral features of different classes of random diffusivity processes
• Moses, Noah and Joseph Effects in Coupled Lévy Processes
• Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories
• Unsupervised learning of anomalous diffusion data
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• Non-Gaussian fluctuations of a probe coupled to a Gaussian field
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• Beyond the universal Dyson singularity for 1-D chains with hopping disorder
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• Target Searches of Interacting Brownian Particles
• Classification of anomalous diffusion in animal movement data using power spectral analysis
• Complete Decomposition of Anomalous Diffusion in Variable Speed Generalized Lévy Walks