{"pk":64908,"title":"Locally uniform random permutations with large increasing subsequences","subtitle":null,"abstract":"We investigate the maximal size of an increasing subset among points randomly sampled from certain probability densities. Kerov and Vershik's celebrated result states that the largest increasing subset among \\(N\\) uniformly random points on \\([0,1]^2\\) has size asymptotically \\(2\\sqrt{N}\\). More generally, the order \\(\\Theta(\\sqrt{N})\\) still holds if the sampling density is continuous. In this paper we exhibit two sufficient conditions on the density to obtain a growth rate equivalent to any given power of \\(N\\) greater than \\(\\sqrt{N}\\), up to logarithmic factors. Our proofs use methods of slicing the unit square into appropriate grids, and investigating sampled points appearing in each box.\n \nMathematics Subject Classifications: 60C05, 05A05\n \nKeywords: Random permutations, longest increasing subsequences, permutons","language":"en","license":{"name":"Creative Commons Attribution 4.0","short_name":"CC BY 4.0","text":"Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.","url":"https://creativecommons.org/licenses/by/4.0"},"keywords":[{"word":"Random permutations"},{"word":"longest increasing subsequences"},{"word":"permutons"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/74p4n0rz","frozenauthors":[{"first_name":"Victor","middle_name":"","last_name":"Dubach","name_suffix":"","institution":"Institut Élie Cartan de Lorraine, Université de Lorraine, Nancy, France","department":""}],"date_submitted":"2023-12-22T13:14:39Z","date_accepted":"2023-12-22T13:14:39Z","date_published":"2023-12-22T08:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64908/galley/49718/download/"}]}