Stationary fluctuations of run-and-tumble particles (Q6601694)

The authors consider a system of independent run-and-tumble particles on \(Z\) and they study the stationary fluctuations of its empirical distribution. In this sense, the paper can be viewed as a study of macroscopic properties of the multi-layer particle systems which was studied by the same authors in [J. Stat. Phys. 190, No. 4, Paper No. 88, 19 p. (2023; Zbl 07687878)].\N\NThe main result is given in Theorem 3.1, where, the authors proved that the joint densities of particles with given internal state converges to a system of stochastic partial differential equations. In these limiting equations, the drift is determined by the hydrodynamic limit (see for example [\textit{C. Erignoux}, Mém. Soc. Math. Fr., Nouv. Sér. 169, 1--202 (2021; Zbl 1475.60196); \textit{S. Floreani} et al., J. Stat. Phys. 186, No. 3, Paper No. 33, 45 p. (2022; Zbl 1483.60067)]), whereas the noise has both a conservative part coming from the transport of particles with a given internal state as well as a non-conservative part coming from the flipping of internal states, (for this part they used some results form [\textit{J.-D. Deuschel} and \textit{D. W. Stroock}, Large deviations. Rev. ed. Boston, MA etc.: Academic Press, Inc. (1989; Zbl 0705.60029)]).