Second Order Freeness and Fluctuations of Random Matrices: I. Gaussian and Wishart matrices and Cyclic Fock spaces

We extend the relation between random matrices and free probability theory from the level of expectations to the level of fluctuations. We introduce the concept of "second order freeness" and derive the global fluctuations of Gaussian and Wishart random matrices by a general limit theorem for second order freeness. By introducing cyclic Fock space, we also give an operator algebraic model for the fluctuations of our random matrices in terms of the usual creation, annihilation, and preservation operators. We show that orthogonal families of Gaussian and Wishart random matrices are asymptotically free of second order.Comment: 46 pages, 13 figures, second revision adds explanations, figures, and reference

FARMERS' PERCEPTIONS OF SPATIAL YIELD VARIABILITY AS INFLUENCED BY PRECISION FARMING INFORMATION GATHERING TECHNOLOGIES

This study evaluated how farmers' perceptions of spatial yield variability are influenced by precision technologies. Farmer estimates from a mail survey were regressed on use of alternative information technologies and personal characteristics. Results indicate that farmers who adopted yield monitors with GPS for cotton perceived significantly higher spatial yield variability.Research and Development/Tech Change/Emerging Technologies,

Hawking's singularity theorem for C1,1C^{1,1}-metrics

We provide a detailed proof of Hawking's singularity theorem in the regularity class $C^{1,1}$, i.e., for spacetime metrics possessing locally Lipschitz continuous first derivatives. The proof uses recent results in $C^{1,1}$-causality theory and is based on regularisation techniques adapted to the causal structure.Comment: 19 pages, LaTeX; v2: corrected Lemma 4.2; v3: typos corrected, final versio