%0 Journal Article %T Spatiotemporal spin fluctuations caused by spin-orbit-coupled Brownian motion %A A. V. Poshakinskiy %A S. A. Tarasenko %J Physics %D 2015 %I arXiv %R 10.1103/PhysRevB.92.045308 %X We develop a theory of thermal fluctuations of spin density emerging in a two-dimensional electron gas. The spin fluctuations probed at spatially separated spots of the sample are correlated due to Brownian motion of electrons and spin-obit coupling. We calculate the spatiotemporal correlation functions of the spin density for both ballistic and diffusive transport of electrons and analyze them for different types of spin-orbit interaction including the isotropic Rashba model and persistent spin helix regime. The measurement of spatial spin fluctuations provides direct access to the parameters of spin-orbit coupling and spin transport in conditions close to the thermal equilibrium. %U http://arxiv.org/abs/1505.03826v1