Discrete Poisson hardcore 1D model and reinfections

TL;DR

This paper introduces a new discrete hardcore Poisson distribution for Young diagrams, employing a 1D Matérn II process, with applications to modeling reinfections in epidemics and connections to Bessel functions.

Contribution

It develops a novel discrete hardcore Poisson distribution for Young diagrams and applies it to epidemic reinfection modeling, offering new formulas and probabilistic insights.

Findings

Distribution expressed via Bessel I-functions

Application to epidemic reinfection modeling

New formulas for truncated Poisson distributions

Abstract

We suggest a new hardcore Poisson-type distribution for Young diagrams with the row lengths from some finite list. A discrete variant of the time-ordered Mat\'{e}rn II process in 1D is employed. This approach is related to that based on the interlacing sequences due to Kerov and others, but we restrict the number of rows. The basic lengths are assumed comparable with the total order of the diagram in the quasi-classical limit, which results in new methods and new formulas. An interesting application is to random walks where the steps are at the points satisfying the classical Poisson distribution or our truncatedone. In the simplest case, one obtains the distribution in terms of Bessel I-functions, which provides some probabilistic interpretation of its many properties. An immediate application of our truncated Poisson distributions is to modeling reinfections in epidemics.