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The problem of the statistics of a set of chaotic vortex lines in acounterflowing superfluid helium is studied. We introduced a Langevin-typeforce into the equation of motion of the vortex line in presence of relativevelocity $\mathbf{v_{ns}}$. This random force is supposed to be Gaussiansatisfying the fluctuation-dissipation theorem. The corresponding Fokker-Planckequation for probability functional in the vortex loop configuration space isshown to have a solution in the form of Gibbs distribution with thesubstitution $E\{\mathbf{s\}\rightarrow }E(\{\mathbf{% s\}-P(v_{n}-v_{s})}$,where $E\{\mathbf{s\}}$ is the energy of the vortex configuration$\{\mathbf{s\}}$, and $\mathbf{P}$ is the Lamb impulse. Some physicalconsequences of this fact are discussed.\\ \newline PACS numbers: 47.32.C-(Vortex dynamics) 47.32.cf (Vortex reconnection and rings), 47.37.+q(Hydrodynamic aspects of superfluidity)

Langevin dynamics of vortex lines in the counterflowing He II. Talk given at the Low Temperature Conference, Kazan, 2015