Geodesic
Jacobi branching random walks corresponding to orthogonal polynomials of discrete variable
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 173-188

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A branching random walk on $\mathbf{Z}_+$ is considered, which corresponds to a Jacobi matrix. Previously, formulas for the average number of particles at an arbitrary fixed point in $\mathbf{Z}_+$ at time $t>0$ were obtained in terms of the orthogonal polynomials associated with this matrix. In the present work, the application of the obtained results to certain models involving orthogonal polynomials of a discrete variable (Krawtchouk, Meixner, and Poisson–Charlier polynomials) is discussed. 
@article{ZNSL_2024_535_a11,
     author = {A. V. Lyulintsev},
     title = {Jacobi branching random walks corresponding to orthogonal polynomials of discrete variable},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {173--188},
     publisher = {mathdoc},
     volume = {535},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a11/}
}
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A. V. Lyulintsev. Jacobi branching random walks corresponding to orthogonal polynomials of discrete variable. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 173-188. http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a11/