Multivariate central limit theorems for Rademacher functionals with applications

Asymptotic for the cumulative distribution function of the degrees and homomorphism densities for random graphs sampled from a graphon

“…In the particular case of the joint distribution of the count of edges, triangles and two-stars, Reinert and Röllin [30], Proposition 2, obtained bounds on the approximation. Using discrete Malliavin calculus, Krokowski and Thäle [18] generalized the result of [30] (in a different probability metric) and get the rate of convergence associated to the multivariate central limit theorem given in [17]. See also Féray, Méliot and Nikeghbali [13], Section 10, for the mod-Gaussian convergence of homomorphism densities.…”