303,816 research outputs found
A hierarchy of Palm measures for determinantal point processes with gamma kernels
The gamma kernels are a family of projection kernels
on a doubly infinite -dimensional lattice. They
are expressed through Euler's gamma function and depend on two continuous
parameters . The gamma kernels initially arose from a model of random
partitions via a limit transition. On the other hand, these kernels are closely
related to unitarizable representations of the Lie algebra
. Every gamma kernel serves as a correlation
kernel for a determinantal measure , which lives on the space of
infinite point configurations on the lattice.
We examine chains of kernels of the form and establish the following
hierarchical relations inside any such chain:
Given , the kernel is a one-dimensional perturbation of
(a twisting of) the kernel , and the one-point Palm
distributions for the measure are absolutely continuous with
respect to .
We also explicitly compute the corresponding Radon-Nikod\'ym derivatives and
show that they are given by certain normalized multiplicative functionals.Comment: Version 2: minor changes, typos fixe
Some considerations in connection with Kurepa's function
In this paper we consider the functional equation for factorial sum and its
particular solutions (Kurepa's function \cite{Kurepa_71} and function
). We determine an extension of domain of functions and
in the sense of Cauchy's principal value at point \cite{Slavic_70}.
In this paper we give an addendum to the proof of Slavi\' c's representation of
Kurepa's function \cite{Slavic_73}. Also, we consider some
representations of functions and via incomplete gamma
function and we consider differential transcendency of previous functions too.Comment: 11 page
Fragmentation functions of mesons in the Field-Feynman model
The fragmentation functions of the pion with distinction between
, , and are studied in the
Field-Feynman recursive model, by taking into account the flavor structure in
the excitation of quark-antiquark pairs by the initial quarks. The obtained
analytical results are compatible with available empirical results. The
framework is also extended to predict the fragmentation functions of the kaon
with distinction between , ,
, and . This work gives a significant
modification of the original model, and the predictions can be tested by future
experiments on the fragmentation functions of the kaon.Comment: 6 Latex pages, 10 figures, to appear in EPJ
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