%0 Journal Article
%T On a Seminal Paper by Karlin and McGregor
%A Mirta M. Castro
%A F. Alberto Grščnbaum
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2013
%I National Academy of Science of Ukraine
%X The use of spectral methods to study birth-and-death processes was pioneered by S. Karlin and J. McGregor. Their expression for the transition probabilities was made explicit by them in a few cases. Here we complete their analysis and indicate a few applications of their very powerful method.
%K birth-and-death processes
%K spectral measure
%U http://dx.doi.org/10.3842/SIGMA.2013.020