Universality of the limit shape of convex lattice polygonal lines

DOI10.1214/10-AOP607zbMath1242.52007arXiv0807.3682OpenAlexW2092887241WikidataQ59902781 ScholiaQ59902781MaRDI QIDQ653304

Sakhavat M. Zarbaliev, Leonid V. Bogachev

Publication date: 9 January 2012

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.3682

zbMATH Keywords

randomizationlocal limit theoremlimit shapeconvex lattice polygonal lines

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Combinatorial aspects of partitions of integers (05A17) Lattices and convex bodies (number-theoretic aspects) (11H06) Random convex sets and integral geometry (aspects of convex geometry) (52A22) Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) (05D40)

Related Items (4)

Unified derivation of the limit shape for multiplicative ensembles of random integer partitions with equiweighted parts ⋮ Asymptotics of convex lattice polygonal lines with a constrained number of vertices ⋮ Limit shape of random convex polygonal lines: even more universality ⋮ Partitions of large unbalanced bipartites

Cites Work

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• Statistical mechanics of combinatorial partitions, and their limit shapes
• A proof of the Vershik-Prohorov conjecture on the universality of the limit shape for a class of random polygonal lines
• Large deviations in the geometry of convex lattice polygons
• Independent process approximations for random combinatorial structures
• Logarithmic combinatorial structures: A probabilistic approach
• Approximation of convex functions by random polygonal lines
• The limit shape of convex lattice polygons
• Probabilistic approach to the analysis of statistics for convex polygonal lines
• The limit shape of convex lattice polygons and related topics
• Combinatorial stochastic processes. Ecole d'Eté de Probabilités de Saint-Flour XXXII -- 2002.
• The Kantorovich metric: the initial history and little-known applications
• A Local Limit Theorem for Random Strict Partitions
• The Structure of Random Partitions of Large Integers
• Limit distribution of the energy of a quantum ideal gas from the viewpoint of the theory of partitions of natural numbers
• Limit theorems for a certain class of random convex polygonal lines
• Clustering in coagulation-fragmentation processes, random combinatorial structures and additive number systems: Asymptotic formulae and limiting laws
• Prescribing a System of Random Variables by Conditional Distributions
• ON THE CONVERGENCE OF EIGENFUNCTION EXPANSIONS

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