We investigate the distribution of single molecule line shape cumulants, ${\kappa }_1,{\kappa }_2,\dots$ , in low temperature glasses based on the sudden jump, standard tunneling model. We find that the cumulants are described by Lévy stable laws, thus the generalized central limit theorem is applicable for this problem.

• Received 21 December 1999

DOI:https://doi.org/10.1103/PhysRevLett.84.5339