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• W2962720904 abstract "In this paper, we study the asymptotics of the degree sequence of permutation graphs associated with a sequence of random permutations. The limiting finite-dimensional distributions of the degree proportions are established using results from graph and permutation limit theories. In particular, we show that for a uniform random permutation, the joint distribution of the degree proportions of the vertices labeled $lceil nr_{1}rceil,lceil nr_{2}rceil,ldots,lceil nr_{s}rceil$ in the associated permutation graph converges to independent random variables $D(r_{1}),D(r_{2}),ldots,D(r_{s})$, where $D(r_{i})simoperatorname{Unif}(r_{i},1-r_{i})$, for $r_{i}in[0,1]$ and $iin{1,2,ldots,s}$. Moreover, the degree proportion of the mid-vertex (the vertex labeled $n/2$) has a central limit theorem, and the minimum degree converges to a Rayleigh distribution after an appropriate scaling. Finally, the asymptotic finite-dimensional distributions of the permutation graph associated with a Mallows random permutation is determined, and interesting phase transitions are observed. Our results extend to other nonuniform measures on permutations as well." @default.
• W2962720904 created "2019-07-30" @default.
• W2962720904 creator A5052870102 @default.
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• W2962720904 date "2017-02-01" @default.
• W2962720904 modified "2023-09-23" @default.
• W2962720904 title "Degree sequence of random permutation graphs" @default.
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• W2962720904 doi "https://doi.org/10.1214/16-aap1207" @default.
• W2962720904 hasPublicationYear "2017" @default.
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