Universality of the limit shape of convex lattice polygonal lines

Details Universality of the limit shape of convex lattice polygonal lines Universality of the limit shape of convex lattice polygonal lines

2008-07-23

arxiv.org/abs/0807.3682v4

Annals of Probability 2011, Vol. 39, No. 6, 2271-2317

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AOP607 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/10-AOP607

Let ${\varPi}_n$ be the set of convex polygonal lines $\varGamma$ with vertices on $\mathbb {Z}_+^2$ and fixed endpoints $0=(0,0)$ and $n=(n_1,n_2)$. We are concerned with the limit shape, as $n\to\infty$, of "typical" $\varGamma\in {\varPi}_n$ with respect to a parametric family of probability measures $\{P_n^r,0

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