Noisy continuous time random walks

TL;DR

This paper extends the continuous time random walk model by adding Gaussian noise, revealing complex behaviors like apparent ergodicity, which aids in analyzing subdiffusive processes in biological environments.

Contribution

It introduces a noisy CTRW model that combines trapping with Gaussian noise, providing a more realistic framework for analyzing biomolecular diffusion.

Findings

Noisy CTRW can appear ergodic despite underlying weak ergodicity breaking.

The model exhibits a variety of dynamic regimes depending on noise strength.

Enhanced understanding of subdiffusive behavior in biological systems.

Abstract

Experimental studies of the diffusion of biomolecules in the environment of biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule trajectories quite intricate. Here we consider subdiffusive continuous time random walks, that represent a seminal model for the anomalous diffusion of tracer particles in complex environments. This motion is characterized by multiple trapping events with infinite mean sojourn time. In real physical situations, however, instead of the full immobilization predicted by the continuous time random walk model, the motion of the tracer particle shows additional jiggling, for instance, due to thermal agitation of the environment. We here present and analyze in detail an extension of the continuous time random walk model. Superimposing the multiple trapping behavior with additive Gaussian noise of variable strength, we demonstrate that the resulting process exhibits a rich variety of apparent dynamic regimes. In particular, such noisy continuous time random walks may appear ergodic while the naked continuous time random walk exhibits weak ergodicity breaking. Detailed knowledge of this behavior will be useful for the truthful physical analysis of experimentally observed subdiffusion.