Asymptotic properties of random matrices and pseudomatrices

We study the asymptotics of sums of matricially free random variables called random pseudomatrices, and we compare it with that of random matrices with block-identical variances. For objects of both types we find the limit joint distributions of blocks and give their Hilbert space realizations, using operators called `matricially free Gaussian operators'. In particular, if the variance matrices are symmetric, the asymptotics of symmetric blocks of random pseudomatrices agrees with that of symmetric random blocks. We also show that blocks of random pseudomatrices are `asymptotically matricially free' whereas the corresponding symmetric random blocks are `asymptotically symmetrically matricially free', where symmetric matricial freeness is obtained from matricial freeness by an operation of symmetrization. Finally, we show that row blocks of square, lower-block-triangular and block-diagonal pseudomatrices are asymptotically free, monotone independent and boolean independent, respectively.Comment: 33 pages, 2 figure

Free analog of pressure and its Legendre transform

The free analog of the pressure is introduced for multivariate noncommutative random variables and its Legendre transform is compared with Voiculescu's microstate free entropy.Comment: Slightly corrected in April 200

THE STUDY OF BIOCHEMICAL PARAMETERS FOR NAVAL ACADEMY TEAM IN THE NAVAL PENTATHLON

Under consideration accomplished subdued research a series of the biochemical parameters (the haemoglobin, albuminoidal, lactic acid), who conditions the physical special effort. Hold the medical area ( A. Demeter, 1982; I. Dragan, 1984; M. Ifrim, 1989, etc.) propose in the process of selection grids with standard values have the parameters determinant in the system criterions of selection. Biochemical investigations suggested were effectuate in this experimentally stage to the initially and final moment. Through these inhibition of laboratory investigation we have follow: 1. If the results obtained frames in the natural suggested limits hold by the medical area specialist; 2. In what grey the investigations values obtained are influenced of the specific complex effort from the military pentathlon. The biochemical investigation realized demonstrated that the results obtained of subjects the group of the experiment they framed in natural physiological limits. From the series four the biochemical parameters apply in research, from statistical viewpoint to the ultimate testing mark crease average values to the level experiment group. "the haemoglobin, albuminoidal, lactic acid, the urea