Thermal Fluctuations of Elastic Ring

We study the effects of thermal fluctuations on a small elastic ring. We derive analytical expressions for the correlation functions of the Euler angles, for the real space two--point correlation functions and for the probability distribution of writhe, as a function of the persistence lengths that determine the rigidity with respect to bending and twist. Fluctuation amplitudes diverge in the limit of vanishing twist rigidity. There is crossover from a small scale regime in which twist and writhe modes are uncoupled, to a large scale regime in which twist affects the spatial configurations of the ring.