离散泊松硬核1D模型和再感染
Discrete Poisson hardcore 1D model and reinfections
摘要：
我们提出了一个新的硬核泊松型分布的杨图的行长度从一些有限的列表。采用一维时间有序Matérn II过程的离散变体。这种方法与Kerov等人提出的基于隔行序列的方法有关，但我们限制了行数。在准经典极限下，假定基本长度与图的总阶可比，从而得到新的方法和新的公式。一个有趣的应用是随机游动，其中的步骤是在满足经典的泊松分布或我们的截断点。在最简单的情况下，人们可以用贝塞尔函数来得到分布，这为它的许多性质提供了一些概率解释。我们的截断泊松分布的一个直接应用是在流行病的再感染建模。
英文摘要：
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 Matérn 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.
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