We study analytically the distribution of the minimum of a set of hierarchically correlated random variables E1, E2, . . ., EN where Ei represents the energy of the i-th path of a directed polymer on a Cayley tree. If the variables were uncorrelated, the minimum energy would have an asymptotic Gumbel distribution. We show that due to the hierarchical correlations, the forward tail of the distri...

The gapped local alignment score of two random sequences follows a Gumbel distribution. If computers could estimate the parameters of the Gumbel distribution within one second, the use of arbitrary alignment scoring schemes could increase the sensitivity of searching biological sequence databases over the web. Accordingly, this article gives a novel equation for the scale parameter of the relev...

Fluctuations of the maximal particle energy of the quantum ideal gas and random partitions Abstract We investigate the limiting distribution of the fluctuations of the maximal summand in a random partition of a large integer with respect to a multiplicative statistics. We show that for a big family of Gibbs measures on partitions (so called generalized Bose–Einstein statistics) this distributio...

Fluctuations of the maximal particle energy of the quantum ideal gas and random partitions Abstract We investigate the limiting distribution of the fluctuations of the maximal summand in a random partition of a large integer with respect to a multiplicative statistics. We show that for a big family of Gibbs measures on partitions (so called generalized Bose–Einstein statistics) this distributio...

We discuss tail behaviors, subexponentiality and extreme value distribution of logarithmic skew-normal random variables. With optimal normalized constants, the asymptotic expansion of the distribution of the normalized maximum of logarithmic skew-normal random variables is derived. It shows that the convergence rate of the distribution of the normalized maximum to the Gumbel extreme value distr...

In this paper, the higher-order asymptotic expansion of the moment of extreme from generalized Maxwell distribution is gained, by which one establishes the rate of convergence of the moment of the normalized partial maximum to the moment of the associate Gumbel extreme value distribution.

A spatially reconfigurable antenna arrays consists of an antenna array of finite length and fixed geometry which is displaced within a given area. Using these reconfigurable components, the performance of MIMO systems is remarkably improved by effectively positioning the array in its displacement area. This paper studies the large-system performance of MIMO setups with spatially reconfigurable ...