Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 9 (2013), 020, 11 pages      arXiv:1303.0361      http://dx.doi.org/10.3842/SIGMA.2013.020

On a Seminal Paper by Karlin and McGregor

Mirta M. Castro a and F. Alberto Grünbaum b
a) Departamento Matemática Aplicada II, Universidad de Sevilla, c\Virgen de África 7, 41011, Sevilla, Spain
b) Department of Mathematics, University of California, Berkeley, Berkeley, CA 94720 USA

Received August 04, 2012, in final form February 25, 2013; Published online March 02, 2013

Abstract
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.

Key words: birth-and-death processes; spectral measure.

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