2017
DOI: 10.1007/s11856-017-1599-3
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Asymptotics of convex lattice polygonal lines with a constrained number of vertices

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Cited by 2 publications
(1 citation statement)
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“…In a different development, a surprising universality result with the same limit shape (3) was obtained by Bureaux and Enriquez [8] under the uniform probability measure on the space of constrained convex lattice polygonal lines with a prescribed number of vertices growing with n, regardless of growth rate. On the other hand, it was demonstrated in [8] that, under additional constraints on the length of the polygonal line, the limit shape modifies to transverse a continuous family of convex curves interpolating between the hypotenuse, and a concatenation of the two legs of the limiting triangular container {0 ≤ x 1 ≤ 1, 0 ≤ x 2 ≤ cx 1 }. Related results were obtained earlier by Bárány [9], Žunić [10], Stojaković [11], and Prodromou [12].…”
Section: Introductionmentioning
confidence: 53%
“…In a different development, a surprising universality result with the same limit shape (3) was obtained by Bureaux and Enriquez [8] under the uniform probability measure on the space of constrained convex lattice polygonal lines with a prescribed number of vertices growing with n, regardless of growth rate. On the other hand, it was demonstrated in [8] that, under additional constraints on the length of the polygonal line, the limit shape modifies to transverse a continuous family of convex curves interpolating between the hypotenuse, and a concatenation of the two legs of the limiting triangular container {0 ≤ x 1 ≤ 1, 0 ≤ x 2 ≤ cx 1 }. Related results were obtained earlier by Bárány [9], Žunić [10], Stojaković [11], and Prodromou [12].…”
Section: Introductionmentioning
confidence: 53%