We study the distribution of the smallest eigenvalue for certain classes of positive-definite Hermitian random matrices, in the limit where the size of the matrices becomes large. Their limit distributions can be expressed as Fredholm determinants of integral operators associated to kernels built out of Meijer G-functions or Wright’s generalized Bessel functions. They generalize in a natural wa...

We shall see that in these cases the spectra come from irreducible representations of G occurring in L2(Γ\G), and that the resulting integral transform of g has a kernel composed of Bessel functions of representations of G. It should be noted that (2) can readily be extended to any imaginary quadratic number field of class number one. Other examples that share the same structure and have been m...

Let P (G, q) be the chromatic polynomial for coloring the n-vertex graph G with q colors, and defineW = limn→∞ P (G, q) 1/n. Besides their mathematical interest, these functions are important in statistical physics. We give a comparative discussion of exact calculations of P and W for a variety of recursive families of graphs, including strips of regular lattices with various boundary condition...

The set of zeros of a Brownian motion gives rise to a product system in the sense of William Arveson (that is, a continuous tensor product system of Hilbert spaces). Replacing the Brownian motion with a Bessel process we get a continuum of non-isomorphic product systems.

Stable ring-profile vortex solitons, featuring a bright shape, appear to be very rare in nature. However, here we show that they exist and can be made dynamically stable in defocusing cubic nonlinear media with an imprinted Bessel optical lattice. We find the families of vortex solitons and reveal their salient properties, including the conditions required for their stability. We show that the ...

In particular we shall first determine a radius of univalence for the normalized Bessel functions [7>(z)]1/" for values of v belonging to the region G defined by the inequalities 6{\v} >0, | arg »»| <7r/4. Then we shall determine the radius of univalence of the functions z1_"7,.(z) for values of v belonging to a subset of the closure of G. When v is real and positive we shall determine the exac...

Recently, it has been observed that a new method for generating continuous&nbsp;distributions, T - X family, can be quite effectively used to analyze the data in one&nbsp;dimension. The aim of this study is to generalize this method to two dimensional&nbsp;space so that the marginals would have T - X distributions. So, several examples and&nbsp;properties of this family have been presented. As ...