The limit shape of convex lattice polygons and related topics

DOI10.1007/BF01079006zbMath0848.52004MaRDI QIDQ1909908

Anatoly M. Vershik

Publication date: 24 March 1996

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

zbMATH Keywords

convexitylattice pointslattice polygonslimit-shape

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Lattices and convex bodies (number-theoretic aspects) (11H06) Erd?s problems and related topics of discrete geometry (52C10) Lattices and convex bodies in (2) dimensions (aspects of discrete geometry) (52C05)

Related Items (22)

Probabilistic approach to the analysis of statistics for convex polygonal lines ⋮ Convex cones, integral zonotopes, limit shape ⋮ CONVEX CURVES AND A POISSON IMITATION OF LATTICES ⋮ Asymptotics of random partitions of a set ⋮ Asymptotics of convex lattice polygonal lines with a constrained number of vertices ⋮ Limit shape of random convex polygonal lines: even more universality ⋮ Region selection in Markov random fields: Gaussian case ⋮ Limit shape of optimal convex Lattice polygons in the sense of different metrics. ⋮ Random points and lattice points in convex bodies ⋮ Universality of the limit shape of convex lattice polygonal lines ⋮ Statistical mechanics of combinatorial partitions, and their limit shapes ⋮ A problem of random choice and its deterministic structure ⋮ On the number of rational points on a strictly convex curve ⋮ The limiting curve of Jarník's polygons ⋮ Beyond Hammersley's last-passage percolation: a discussion on possible local and global constraints ⋮ A proof of the Vershik-Prohorov conjecture on the universality of the limit shape for a class of random polygonal lines ⋮ Approximation of convex sets by polytopes ⋮ Large deviations in the geometry of convex lattice polygons ⋮ Large deviations of convex polyominoes ⋮ Limit shape of convex lattice polygons having the minimal \(L_\infty\) diameter w. r. t. the number of their vertices ⋮ Limit shape of convex lattice polygons with minimal perimeter ⋮ On Finding The Limit Shape Of Optimal Convex Lattice Polygons

Cites Work

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• Zur additiven Zahlentheorle in mehreren Dimensionen. I
• Integer points on curves and surfaces
• Probabilistic approach to the analysis of statistics for convex polygonal lines
• On the number of convex lattice polytopes
• The number of integral points on arcs and ovals
• The Number of Partitions of a Large Bi-Partite Number
• Convex bodies, economic cap coverings, random polytopes
• A Lower Bound for the Volume of Strictly Convex Bodies with many Boundary Lattice Points

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