Longest increasing paths with gaps
العنوان: | Longest increasing paths with gaps |
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المؤلفون: | Anne-Laure Basdevant, Lucas Gerin |
المساهمون: | Modélisation aléatoire de Paris X (MODAL'X), Université Paris Nanterre (UPN), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), ANR-14-CE25-0014,GRAAL,GRaphes et Arbres ALéatoires(2014), ANR-16-CE40-0016,PPPP,Percolation et percolation de premier passage(2016), ANR-16-CE93-0003,MALIN,Marches aléatoires en interaction(2016) |
المصدر: | ALEA : Latin American Journal of Probability and Mathematical Statistics ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2019, 16 (2), pp.1141--1163 ALEA : Latin American Journal of Probability and Mathematical Statistics, 2019, 16 (2), pp.1141--1163 |
بيانات النشر: | arXiv, 2018. |
سنة النشر: | 2018 |
مصطلحات موضوعية: | Statistics and Probability, combinatorial probability, 01 natural sciences, Point process, 010104 statistics & probability, Bernoulli's principle, Ordinate, Mathematics::Probability, 0103 physical sciences, Poisson point process, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, Mathematics - Combinatorics, 0101 mathematics, Ulam's problem, 60K35, 60F15, Mathematics, Mathematical analysis, Probability (math.PR), last-passage percolation, longest increasing paths, Limiting, longest increasing subsequences, Hammersley's process, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Distribution (mathematics), Percolation, BLIP (Bernoulli Longest In-creasing Paths), Path (graph theory), 010307 mathematical physics, Combinatorics (math.CO), Mathematics - Probability |
الوصف: | International audience; We consider a variant of the continuous and discrete Ulam-Hammersley problems: we study the maximal length of an increasing path through a Poisson point process (or a Bernoulli point process) with the restriction that there must be minimal gaps between abscissae and ordinates of successive points of the path.For both cases (continuous and discrete) our approach rely on couplings with well-studied models: respectively the classical Ulam-Hammersley problem and last-passage percolation with geometric weights. Thanks to these couplings we obtain explicit limiting shapes in both settings.We also establish that, as in the classical Ulam-Hammersley problem, the fluctuations around the mean are given by the Tracy-Widom distribution. |
تدمد: | 1980-0436 |
DOI: | 10.48550/arxiv.1805.09136 |
URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::40ead9762e06986d84b309db3934648b |
حقوق: | OPEN |
رقم الأكسشن: | edsair.doi.dedup.....40ead9762e06986d84b309db3934648b |
قاعدة البيانات: | OpenAIRE |
تدمد: | 19800436 |
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DOI: | 10.48550/arxiv.1805.09136 |