2008 SEP 22 - (VerticalNews.com) -- "We consider branching random walks in d-dimensional integer lattice with time-space i.i.d. offspring distributions," investigators in Kyoto, Japan report.

  "When d> 3 and the fluctuation of the environment is well moderated by the random walk, we prove a central limit theorem for the density of the population, together with upper bounds for the density of the most populated site and the replica overlap," wrote N. Yoshida and colleagues, Kyoto University ...read more

  2008 SEP 22 - (VerticalNews.com) -- According to a study from Haifa, Israel, "Given a random variable N with values in N, and N i.i.d. positive random variables (AkI, we consider a queue with renewal arrivals and N exponential servers, where server k serves at rate Ak, under two work conserving routing schemes. In the first, the service rates 1141 need not be known to the router, and each customer to arrive at a time when some servers are idle is routed to the server that has been idle for the longest time (or otherwise it is queued). ...read more

  2008 JUL 21 - (VerticalNews.com) -- According to a study from Netherlands, "Let s(k) = 1/root N(nu(1k),...,nu(Nk))(T), with {nu(ik),i,k = 1,...} independent and, identically distributed complex random variables. Write S-k = (s(1),..., s(k-1), s(k+1),...,s(K)), P-k = diag(p(1),...,p(k-1), p(k+l), p(K)), R-k = (SkPkSk* + sigma I-2) and A(km) = [s(k), R(k)s(k),..., R(k)(m-1)s(k)]."

  "Define beta(km) = p(k)s(k)*A(km)(A(km)* x R(k)Ak(m))(-1)A(km)*s(k), referred to as the signal-to-interference ratio (SIR) of user k k under the multistage Wiener (MSW) receiver in a wireless communication system. It is proved that the output SIR under the MSW and the mutual information statistic under the matched filter (MF) are both asymptotic Gaussian when N/K -> c> 0. Moreover, we provide a central limit theorem for linear spectral statistics of eigenvalues and eigenvectors of sample covariance matrices, which is a supplement of Theorem 2 in Bai, Miao and Pan [Ann. Probab. 35 (2007) 1532-1572]," wrote G.M. Pan and colleagues ...read more