An invariance principle related to a process which generalizes the \(N\)-dimensional Brownian motion (Q1433392)

Dunkl differential-difference operators Laplacian and process have recently aroused a great deal of interest from both analytical and probabilistic viewpoints. If \(k\) is a nonnegative multiplicity function defined on a root system in a finite-dimensional Euclidean space, the authors introduce a \(k\)-invariant random walk. Under simple hypotheses, they prove that a suitable normalization of the random walk converges in distribution to the Dunkl process as in the Donsker theorem.