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Fixed points and cycle structure of random permutations. (English) Zbl 1343.05011
Summary: Using the recently developed notion of permutation limits this paper derives the limiting distribution of the number of fixed points and cycle structure for any convergent sequence of random permutations, under mild regularity conditions. In particular this covers random permutations generated from Mallows model with Kendall’s tau, $$\mu$$ random permutations introduced in [C. Hoppen et al., J. Comb. Theory, Ser. B 103, No. 1, 93–113 (2013; Zbl 1255.05174)], as well as a class of exponential families introduced in [S. Mukherjee, Ann. Stat. 44, No. 2, 853–875 (2016; Zbl 1341.62083)].

##### MSC:
 05A05 Permutations, words, matrices 60C05 Combinatorial probability 60F05 Central limit and other weak theorems 62F12 Asymptotic properties of parametric estimators 62F10 Point estimation
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