# Non-scaling displacement distributions as may be seen in fluorescence correlation spectroscopy

## TL;DR

This paper explores a CTRW model with Levy-stable waiting times that produces non-Gaussian, non-scaling diffusion, affecting fluorescence correlation spectroscopy measurements and the interpretation of diffusion coefficients.

## Contribution

It introduces a theoretical model showing how non-scaling, non-Gaussian diffusion impacts FCS analysis and the estimation of diffusion coefficients.

## Key findings

- Displacement distributions are explicitly time-dependent and non-scaling.
- FCS autocorrelation curves can detect deviations from Gaussian diffusion.
- Fitted diffusion coefficients may significantly differ from true values.

## Abstract

A continuous time random walk (CTRW) model with waiting times following the Levy-stable distribution with exponential cut-off in equilibrium is a simple theoretical model giving rise to normal, yet non-Gaussian diffusion. The distribution of the particle displacements is explicitly time-dependent and does not scale. Since fluorescent correlation spectroscopy (FCS) is often used to investigate diffusion processes, we discuss the influence of this lack of scaling on the possible outcome of the FCS measurements and calculate the FCS autocorrelation curves for such equilibrated CTRWs. The results show that although the deviations from Gaussian behavior may be detected when analyzing the short and long-time asymptotic behavior of the corresponding curves, their bodies are still perfectly fitted by the fit forms used for normal diffusion. The diffusion coefficients obtaied from the fits may however differ considerably from the true tracer diffusion coefficients as describing the time dependence of the mean squared displacement