On Bessel Distributions forGL2over ap-Adic Field

Beta Bessel distributions

Three new distributions on the unit interval [0,1] are introduced which generalize the standard beta distribution. These distributions involve the Bessel function. Expression is derived for their shapes, particular cases, and the nthmoments. Estimation by themethod of maximum likelihood and Bayes estimation are discussed. Finally, an application to consumer price indices is illustrated to show ...

Some Distributions Involving Bessel Functions

Maximum Distributions of Noncolliding Bessel Bridges

The one-dimensional Brownian motion starting from the origin at time t = 0, conditioned to return to the origin at time t = 1 and to stay positive during time interval 0 < t < 1, is called the Bessel bridge with duration 1. We consider theN -particle system of such Bessel bridges conditioned never to collide with each other in 0 < t < 1, which is the continuum limit of the vicious walk model in...

Level Spacing Distributions and the Bessel Kernel

Scaling models of random N x N hermitian matrices and passing to the limit N -» oo leads to integral operators whose Fredholm determinants describe the statistics of the spacing of the eigenvalues of hermitian matrices of large order. For the Gaussian Unitary Ensemble, and for many others' as well, the kernel one obtains by scaling in the "bulk" of the spectrum is the "sine kernel" — — . Rescal...

Bessel integrals in epsilon expansion: Squared spherical Bessel functions averaged with Gaussian power-law distributions

Keywords: Squared spherical Bessel functions Regularization of Hankel series Gaussian power-law densities Kummer distributions Airy approximation of Bessel integrals a b s t r a c t Bessel integrals of type R 1 0 k lþ2 e Àak 2 ÀðbþixÞk j 2 l ðpkÞdk are studied, where the squared spherical Bessel function j 2 l is averaged with a modulated Gaussian power-law density. These inte-grals define the ...