Multivariate Kawtchouk polynomials as Birth and Death polynomials

2023/05/15 by Sasaki, Ryu
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2305.08581

Abstract

Multivariate Krawtchouk polynomials are constructed explicitly as Birth and Death polynomials, which have the nearest neighbour interactions. They form the complete set of eigenpolynomials of a birth and death process with the birth and death rates at population x=(x₁,…,x_n) are B_j(x)=(N-∑_i=1ⁿx_i) and D_j(x)=p_i^-1x_j, 0

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