The hard-gluonic contribution to the first moment of the polarized proton structure function g 1(x) is dependent of the factorization convention chosen in defining the quark spin density and the hard cross section for photon-gluon scattering. Two extremes of interest, namely gauge-invariant and chiral-invariant factorization schemes, are considered. We show that in order to satisfy the positivi...

Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various such distribution functions in the limits where certain scaling variables become small or large. Our study includes the pair-connection probability, the distribut...

We consider the functional equation f(t) = 1 b b?1 X =0 f t ? a for all t 2 IR; (F) where 0 < a < 1, b 2 IN n f1g and ?1 = 0 1 : : : b?1 = 1 are given parameters, f : IR ! IR is the unknown. We show that there is a unique bounded function f which solves (F) and satisses f(t) = 0 for t < ?1=(1 ? a), f(t) = 1 for t > 1=(1 ? a). This solution can be interpreted as the distribution function of a ce...

We solve the moment problem for convex distribution functions on [0, 1] in terms of completely alternating sequences. This complements a recent solution of this problem by Diaconis and Freedman, and relates this work to the Lévy-Khintchine formula for the Laplace transform of a subordinator, and to regenerative composition structures.