On a Seminal Paper by Karlin and McGregor

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2013
• Main Authors: Castro, M.M., Grünbaum, F.A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2013
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149212
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On a Seminal Paper by Karlin and McGregor / M.M. Castro, F.A. Grünbaum // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 30 назв. — англ.

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.