Evolution and models for skewed parton distributions

We discuss the structure of the "forward visible" (FV) parts of double and skewed distributions related to the usual distributions through reduction relations. We use factorized models for double distributions (DD's) (f) over bar(x,alpha) in which one factor coincides with the usual (forward) parton distribution and another specifies the profile characterizing the spread of the longitudinal momentum transfer. The model DD's are used to construct skewed parton distributions (SPD's). For small skewedness, the FV parts of SPD's H((x) over bar,xi) can be obtained by averaging forward parton densities f((x) over bar - xi alpha) with the weight p(alpha) coinciding with the profile function of the double distribution (f) over bar(x,alpha) at small x. We show that if the x(n) moments (f) over bar (n)(alpha) of DD's have the asymptotic (1 - alpha(2))(n + 1) profile, then the alpha profile of (f) over bar(x,alpha) far small x is completely determined by the small-x behavior of the usual parton distribution. We demonstrate that, for small xi, the model with asymptotic profiles for (f) over bar(a) is equivalent to that proposed recently by Shuvaev et al., in which the Gegenbauer moments of SPD's do not depend on xi. We perform a numerical investigation of the evolution patterns of SPD's and give an interpretation, of the results of these studies within the formalism of double distributions.