The renormalization-group flow on the affine Virasoro space is considered. The case of fixed points, endowed with sporadic marginal deformations and forming in the ansatz space the manifold G(c) (R(r)), is studied in detail. The explicit form of the statistics transmutation of the primary vertex fields under the action of the renormalization group is found. A comparison with the theory of the bosonic string is given. Possible application to the fractional quantum Hall effect is discussed.