Stochastic gyration driven by dichotomous noises

Timothée Herbeau; Leonid Pastur; Pascal Viot; Gleb Oshanin

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arXiv · 2510.13589

Stochastic gyration driven by dichotomous noises

Timothée Herbeau·Leonid Pastur·Pascal Viot·Gleb Oshanin

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Abstract

We consider stochastic dynamics of a particle on a plane in presence of two noises and a confining parabolic potential - an analog of the experimentally-relevant Brownian Gyrator (BG) model. In contrast to the standard BG model, we suppose here that the time-evolution of the position components is driven not by Gaussian white-noises, but by two statistically-independent dichotomous noises. We calculate analytically the position variances and cross-correlations, as well as the mean angular momentum, which permits us to establish the conditions in which a spontaneous rotational motion of the particle around the origin takes place. We also present a numerical analysis of the mean angular velocity. Lastly, we calculate analytically some marginal position probability density functions revealing a remarkably rich behavior that emerges in such a system of two coupled linear stochastic differential equations. We show that depending on the values of parameters characterizing noises these distributions approach the steady-state forms defined on a finite support, having very unusual shapes, possessing multiple maxima and minima, plateaus and exhibiting a discontinuous behavior.

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Timothée Herbeau, Leonid Pastur, Pascal Viot, Gleb Oshanin. 2025-10-15. Stochastic gyration driven by dichotomous noises. https://arxiv.org/abs/2510.13589

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