Asymptotic properties of the algebraic moment range process

Let M _n denote the n-th moment space of the set of all probability measures on the interval [0, 1], P _n the uniform distribution on the set M _n and r _{n + 1} the maximal range of the (n + 1)-th moments corresponding to a random moment point C _n with distribution P _n on M _n . We study several asymptotic properties of the stochastic process (r _⌊nt⌋+1) _t∈[0,T] if n → ∞. In particular weak convergence to a Gaussian process and a large deviation principle are established.