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Orthogonality and probability: beyond nearest neighbor transitions

2008/12/09 by Yevgeniy Kovchegov, Kovchegov, Yevgeniy
Computer Science · Mathematics · #05E35 #60G05 #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #FOS: Mathematics #Mathematical functions and polynomials #Probability (math.PR) #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.0812.1779

openalex publication_date 2008/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we will explore why Karlin-McGregor method of using orthogonal polynomials in the study of Markov processes was so successful for one dimensional nearest neighbor processes, but failed beyond nearest neighbor transitions. We will proceed by suggesting and testing possible fixtures.

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