The lognormal-like statistics of a stochastic squeeze process

TL;DR

This paper provides an exact analysis of the full statistics of a stochastic squeeze process, revealing non-Gaussian features and complex dependencies in the radial coordinate's distribution that go beyond simple lognormal models.

Contribution

The authors derive exact expressions for the drift and diffusion of log(r) in a stochastic squeeze process, highlighting deviations from heuristic lognormal assumptions and the influence of non-Gaussian tails.

Findings

Radial diffusion depends non-monotonically on parameters w and D.

Distribution tails dominate the moments of log(r).

Results extend beyond the central limit theorem approximation.

Abstract

We analyze the full statistics of a stochastic squeeze process. The model's two parameters are the bare stretching rate~$w$, and the angular diffusion coefficient~$D$. We carry out an exact analysis to determine the drift and the diffusion coefficient of $\log(r)$, where $r$ is the radial coordinate. The results go beyond the heuristic lognormal description that is implied by the central limit theorem. Contrary to the common "Quantum Zeno" approximation, the radial diffusion is not simply $D_r = (1/8)w^2/D$, but has a non-monotonic dependence on $w/D$. Furthermore, the calculation of the radial moments is dominated by the far non-Gaussian tails of the $\log(r)$ distribution.