The following sections are included: Introduction and statement of the problem; Random variables in CeHeis (1); Infinite divisibility; Kernels and matrices; Positive definite kernels; Functions of positive definite matrices and kernels; Conditionally positive definite kernels; Infinitely divisible kernels; The Kolmogorov decomposition theorem for –valued PD kernels; Boson Fock spaces; Infinitely divisible kernels and Boson Fock spaces; References