Asymptotic Distribution of Parameters in Random Maps

DOI10.4230/LIPIcs.AofA.2018.13zbMath1482.05062arXiv1802.07112MaRDI QIDQ4993535

Hsien-Kuei Hwang, Olivier Bodini, Julien Courtiel, Sergey Dovgal

Publication date: 15 June 2021

Full work available at URL: https://arxiv.org/abs/1802.07112

zbMATH Keywords

generating functionsRiccati equationlimit lawspatternsrooted mapsanalytic combinatoricsrandom mapsbeta law

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Planar graphs; geometric and topological aspects of graph theory (05C10)

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Cites Work

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• A central limit theorem for the number of degree-\(k\) vertices in random maps
• Asymptotics and random sampling for BCI and BCK lambda terms
• Terminal chords in connected chord diagrams
• Indecomposable permutations, hypermaps and labeled Dyck paths
• On convergence rates in the central limit theorems for combinatorial structures
• A pattern of asymptotic vertex valency distributions in planar maps
• Rooted maps on orientable surfaces, Riccati's equation and continued fractions
• Counting coloured planar maps: differential equations
• Polynomial equations with one catalytic variable, algebraic series and map enumeration
• Random maps, coalescing saddles, singularity analysis, and Airy phenomena
• A correspondence between rooted planar maps and normal planar lambda terms
• Asymptotics of poisson approximation to random discrete distributions: an analytic approach