Cycle structure of random parking functions
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Publication:6391436
DOI10.1016/J.AAM.2022.102458arXiv2202.08829MaRDI QIDQ6391436
Publication date: 17 February 2022
Abstract: We initiate the study of the cycle structure of uniformly random parking functions. Using the combinatorics of parking completions, we compute the asymptotic expected value of the number of cycles of any fixed length. We obtain an upper bound on the total variation distance between the joint distribution of cycle counts and independent Poisson random variables using a multivariate version of Stein's method via exchangeable pairs. Under a mild condition, the process of cycle counts converges in distribution to a process of independent Poisson random variables.
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