Run-and-tumble oscillator: moment analysis of stationary distributions

Derek Frydel

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arXiv · 2309.12537

Run-and-tumble oscillator: moment analysis of stationary distributions

Derek Frydel

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Abstract

When it comes to active particles, even an ideal-gas model in a harmonic potential poses a mathematical challenge. An exception is a run-and-tumble model (RTP) in one-dimension for which a stationary distribution is known exactly. The case of two-dimensions is more complex but the solution is possible. Incidentally, in both dimensions the stationary distributions correspond to a beta function. In three-dimensions, a stationary distribution is not known but simulations indicate that it does not have a beta function form. The current work focuses on the three-dimensional RTP model in a harmonic trap. The main result of this study is the derivation of the recurrence relation for generating moments of a stationary distribution. These moments are then used to recover a stationary distribution using the Fourier-Lagrange expansion.

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Derek Frydel. 2023-09-21. Run-and-tumble oscillator: moment analysis of stationary distributions. https://arxiv.org/abs/2309.12537

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