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- W4213418259 abstract "Abstract We investigate random minimal factorizations of the n -cycle, that is, factorizations of the permutation $(1 , 2 cdots n)$ into a product of cycles $tau_1, ldots, tau_k$ whose lengths $ell(tau_1), ldots, ell(tau_k)$ satisfy the minimality condition $sum_{i=1}^k(ell(tau_i)-1)=n-1$ . By associating to a cycle of the factorization a black polygon inscribed in the unit disk, and reading the cycles one after another, we code a minimal factorization by a process of colored laminations of the disk. These new objects are compact subsets made of red noncrossing chords delimiting faces that are either black or white. Our main result is the convergence of this process as $n rightarrow infty$ , when the factorization is randomly chosen according to Boltzmann weights in the domain of attraction of an $alpha$ -stable law, for some $alpha in (1,2]$ . The limiting process interpolates between the unit circle and a colored version of Kortchemski’s $alpha$ -stable lamination. Our principal tool in the study of this process is a new bijection between minimal factorizations and a model of size-conditioned labeled random trees whose vertices are colored black or white, as well as the investigation of the asymptotic properties of these trees." @default.
- W4213418259 created "2022-02-25" @default.
- W4213418259 creator A5073158231 @default.
- W4213418259 date "2022-02-24" @default.
- W4213418259 modified "2023-10-14" @default.
- W4213418259 title "Random stable-type minimal factorizations of the <i>n</i>-cycle" @default.
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- W4213418259 doi "https://doi.org/10.1017/apr.2021.21" @default.
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