A. M. Vershik, “The Limit Shape of Convex Lattice Polygons and Related Topics”, Funktsional. Anal. i Prilozhen., 28:1 (1994), 16–25; Funct. Anal. Appl., 28:1 (1994), 13

Citation in format AMSBIB

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\by A.~M.~Vershik

\paper The Limit Shape of Convex Lattice Polygons and Related Topics

\jour Funktsional. Anal. i Prilozhen.

\yr 1994

\vol 28

\issue 1

\pages 16--25

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\transl

\jour Funct. Anal. Appl.

\yr 1994

\vol 28

\issue 1

\pages 13--20

\crossref{https://doi.org/10.1007/BF01079006}

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This publication is cited in the following 28 articles:

Ludovic Morin, “Probability that n points are in convex position in a regular κ-gon: Asymptotic results”, Adv. Appl. Probab., 2025, 1
Ilya Soloveychik, Vahid Tarokh, “Region selection in Markov random fields: Gaussian case”, Journal of Multivariate Analysis, 196 (2023), 105178
Leonid V. Bogachev, Sakhavet M. Zarbaliev, “Inverse Limit Shape Problem for Multiplicative Ensembles of Convex Lattice Polygonal Lines”, Mathematics, 11:2 (2023), 385
Ilya Soloveychik, Vahid Tarokh, “Large deviations of convex polyominoes”, Electron. J. Probab., 27:none (2022)
Imre Bárány, Julien Bureaux, Ben Lund, “Convex cones, integral zonotopes, limit shape”, Advances in Mathematics, 331 (2018), 143
Julien Bureaux, Nathanaël Enriquez, “Asymptotics of convex lattice polygonal lines with a constrained number of vertices”, Isr. J. Math., 222:2 (2017), 515
F. L. Chernousko, A. I. Ovseevich, “A problem of random choice and its deterministic structure”, Dokl. Math., 94:2 (2016), 587
V. M. Buchstaber, M. I. Gordin, I. A. Ibragimov, V. A. Kaimanovich, A. A. Kirillov, A. A. Lodkin, S. P. Novikov, A. Yu. Okounkov, G. I. Olshanski, F. V. Petrov, Ya. G. Sinai, L. D. Faddeev, S. V. Fomin, N. V. Tsilevich, Yu. V. Yakubovich, “Anatolii Moiseevich Vershik (on his 80th birthday)”, Russian Math. Surveys, 69:1 (2014), 165–179
Bogachev L.V., “Limit Shape of Random Convex Polygonal Lines: Even More Universality”, J. Comb. Theory Ser. A, 127 (2014), 353–399
Gravin N. Petrov F. Robins S. Shiryaev D., “Convex Curves and a Poisson Imitation of Lattices”, Mathematika, 60:1 (2014), 139–152
Bogachev L.V., Zarbaliev S.M., “Universality of the Limit Shape of Convex Lattice Polygonal Lines”, Ann Probab, 39:6 (2011), 2271–2317
Bogachev L.V., Zarbaliev S.M., “A proof of the Vershik-Prohorov conjecture on the universality of the limit shape for a class of random polygonal lines”, Dokl. Math., 79:2 (2009), 197–202
E. M. Bronshtein, “Approximation of Convex Sets by Polytopes”, Journal of Mathematical Sciences, 153:6 (2008), 727–762
Krapivsky, PL, “Smoothing a rock by chipping”, Physical Review E, 75:3 (2007), 031119
F. V. Petrov, “Estimates for the number of rational points on convex curves and surfaces”, J. Math. Sci. (N. Y.), 147:6 (2007), 7218–7226
F. V. Petrov, “On the Number of Rational Points on a Strictly Convex Curve”, Funct. Anal. Appl., 40:1 (2006), 24–33
Maria N. Prodromou, “Limit shape of convex lattice polygons with minimal perimeter”, Discrete Mathematics, 300:1-3 (2005), 139
A. M. Vershik, Yu. V. Yakubovich, “The limit shape and fluctuations of random partitions of naturals with fixed number of summands”, Mosc. Math. J., 1:3 (2001), 457–468
L. V. Bogachev, S. M. Zarbaliev, “Limit theorems for a certain class of random convex polygonal lines”, Russian Math. Surveys, 54:4 (1999), 830–832
Vershik, A, “Large deviations in the geometry of convex lattice polygons”, Israel Journal of Mathematics, 109 (1999), 13