The local eigenvalue statistics of large random matrices near a hard edge transitioning into soft are described by the Bessel process associated with parameter ?. For this point process, we obtain (1) exponential moment asymptotics, up to and including constant term, (2) asymptotics for expectation variance counting function, (3) several central limit theorems (4) global rigidity upper bound.

Moment functions de0ned using a polar coordinate representation of the image space, such as radial moments and Zernike moments, are used in several recognition tasks requiring rotation invariance. However, this coordinate representation does not easily yield translation invariant functions, which are also widely sought after in pattern recognition applications. This paper presents a mathematica...

We study Wigner ensembles of symmetric random matrices A = (a ij) i; j = 1; : : : ; n with matrix elements a ij ; i j being independent symmetrically distributed random variables a ji = ij n 1 2 : We assume that Var ij = 1 4 , for i < j, Var ii 6const and that all higher moments of ij also exist and grow not faster than the Gaussian ones. Under formulated conditions we prove the central limit t...

Traditionally, statistical summaries of categorical data often have been visualized using graphical plots of central moments (e.g., mean and standard deviation), or cumulants (e.g., median and quartiles) by box plots. In this work we reexamine the box plot and its relatives and develop a new hybrid summary plot that combines moment, cumulant, and density information. In view of the important ro...

In this paper, a proposed system for classify Islamic geometric patterns with emphasis on representation and recognition stages is introduced. Finding a unique feature for classify IGPs is a hard work that hasn’t been done since today because of the diversity of their different structure. To implement this technique, we use shape based classification. Geometric central moments have been utilize...