In the present work we study hydrodynamic fluctuations in the Gubser flow which serves as a model of expansion of quark-gluon plasma in collisions of heavy ion nuclei at high energies. We present a modern view of hydrodynamics, write down the relativistic hydrodynamic equations and describe the treatment of relativistic hydrodynamic fluctuations. We state some properties of conformal hydrodynamics and introduce two models of quark-gluon plasma expansion after the collision, namely the Bjorken and the Gubser flow. In the case of the Gubser flow, we calculate the corrections to the stress-energy tensor expectation value by taking into account thermal fluctuations. We find three different contributions, two that renormalize energy density and viscosity and a finite term that introduces long-time tails into the relaxation of hydrodynamic correlation functions.
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