Many axiomatic definitions of entropy, such as the Rényi entropy, of a random variable are closely related to the `α-norm of its probability distribution. This study considers probability distributions on finite sets, and examines the sharp bounds of the `β-norm with a fixed `α-norm, α 6= β, for n-dimensional probability vectors with an integer n ≥ 2. From the results, we derive the sharp bound...

Let X be a d×d symmetric random matrix with independent but non-identically distributed Gaussian entries. It has been conjectured by Lata la that the spectral norm of X is always of the same order as the largest Euclidean norm of its rows. A positive resolution of this conjecture would provide a sharp understanding of the probabilistic mechanisms that control the spectral norm of inhomogeneous ...

Cognitive radio (CR) systems make efficient use of the frequency spectrum by opportunistically exploiting unoccupied or under–utilized frequency bands. However, the frequency bands used by CR systems are expected to suffer from various forms of noise and interference with non–Gaussian distributions, such as narrowband and co–channel interference caused by the primary user and other CRs, respect...

Abstract. Gaussian beams are asymptotically valid high frequency solutions to hyperbolic partial differential equations, concentrated on a single curve through the physical domain. They can also be extended to some dispersive wave equations, such as the Schrödinger equation. Superpositions of Gaussian beams provide a powerful tool to generate more general high frequency solutions that are not n...

Distributed wireless sensor networks have been proposed as a solution to environment sensing, target tracking, data collection and other applications. Energy efficiency, high estimation accuracy, and fast convergence are important goals in distributed estimation algorithms for sensor network. This paper studies the problem of robust adaptive estimation in impulsive noise environment using robus...

If the Euclidean norm | · | is strongly concentrated with respect to a measure μ, the average distribution of an average marginal of μ has Gaussian asymptotics that captures tail behaviour. If the marginals of μ have exponential moments, Gaussian asymptotics for the distribution of the average marginal implies Gaussian asymptotics for the distribution of most individual marginals. We show appli...