Renormalization group limits for Wick polynomials of Gaussian processes

Abstract

We consider sequences of Gaussian stationary generalized stochastic processes, admitting formation of Wick polynomials, which converge to infrared singular limit processes for which the Wick powers are not defined. Nevertheless the suitably renormalized Wick polynomials are convergent, the limit processes form a dense set in the space of superpositions of Gaussian processes, i.e. their characteristic functional has the form L(ϕ)=ʃexp{− 1 2 y 2<ϕ|ϕ>}dv(y) where v is a probability measure. In the probabilistic version of renormalization group for continuous systems the sequences can be viewed as orbits under RG transformations having a short scale fixed point.