THE BROWNIAN LIMIT OF SEPARABLE PERMUTATIONS

• 成果类型: Article
• 署名作者: Bassino, Frederique; Bouvel, Mathilde; Feray, Valentin; Gerin, Lucas; Pierrot, Adeline
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); Universite Paris 13; University of Zurich; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1223
• 发表日期: 2018
• 页码: 2134-2189
• 关键词: pattern-avoiding permutations; occurrences; number; trees

摘要

We study uniform random permutations in an important class of pattern-avoiding permutations: the separable permutations. We describe the asymptotics of the number of occurrences of any fixed given pattern in such a random permutation in terms of the Brownian excursion. In the recent terminology of permutons, our work can be interpreted as the convergence of uniform random separable permutations towards a Brownian separable permuton.