Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/317025 
Authors: 
Year of Publication: 
2023
Citation: 
[Journal:] Metrika [ISSN:] 1435-926X [Volume:] 87 [Issue:] 2 [Publisher:] Springer Berlin Heidelberg [Place:] Berlin/Heidelberg [Year:] 2023 [Pages:] 155-182
Publisher: 
Springer Berlin Heidelberg, Berlin/Heidelberg
Abstract: 
Abstract We review a recent development at the interface between discrete mathematics on one hand and probability theory and statistics on the other, specifically the use of Markov chains and their boundary theory in connection with the asymptotics of randomly growing permutations. Permutations connect total orders on a finite set, which leads to the use of a pattern frequencies. This view is closely related to classical concepts of nonparametric statistics. We give several applications and discuss related topics and research areas, in particular the treatment of other combinatorial families, the cycle view of permutations, and an approach via exchangeability.
Subjects: 
Asymptotics
Boundary theory
Copulas
Exchangeability
Markov chains
Permutations
Pattern frequencies
Ranks
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Creative Commons License: 
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Document Type: 
Article
Document Version: 
Published Version
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