A central limit theorem for convex chains in the square

Discrete and Computational Geometry

Volumn 23, Issue 1, 2000, Pages 35-50

  Barany I ^a   Rote, G ^b   Steiger, W ^c   Zhang, C H ^d  

^a ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS   (Hungary)

^b GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^c RUTGERS UNIVERSITY   (United States)

^d RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034400871     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00009490     Document Type: Article

References (12)

1. I. Bárány, The limit shape of convex lattice polygons, Discrete Comput. Geom. 13 (1995), 270-295.
2. I. Bárány, Affine perimeter and limit shape, J. reine angew. Math. 484 (1997), 71-84.
3. I. Bárány, Sylvester's question: the probability that n points are in convex position, Preprint, 1997.
4. Y. S. Chow and H. Teicher, Probability Theory, Springer-Verlag, New York, 1978.
5. P. L. Hsu and H. Robbins, Complete convergence and the law of large numbers. Proc. Nat. Acad. Sci. 33 (1947), 229-240.
6. M. Ledoux, On Talagrand's deviation inequalities for product measures, ESAIM: Probab. Statist. 1 (1995/97), Art. 4, 63-87 (electronic). http://www.emath.fr/Maths/Ps/Articles/psEng-Vol1.4.html
7. Ya. G. Sinai, Probabilistic approach to the analysis of statistics for convex polygonal curves, Funktsional Anal. i Prilozhen. 28(2) (1994), 41-48 (in Russian). English translation in Functional Anal. Appl. 28 (1994), 108-113.
8. Ya. G. Sinai, Probabilistic approach to the analysis of statistics for convex polygonal curves, Funktsional Anal. i Prilozhen. 28(2) (1994), 41-48 (in Russian). English translation in Functional Anal. Appl. 28 (1994), 108-113.
9. P. Valtr, Probability that n random points are in convex position, Discrete Comput. Geom. 13 (1995), 637-643.
10. A. van der Vaart and J. A. Wellner, Weak Convergence and Empirical Processes, Springer-Verlag, New York, 1996.
11. A. M. Vershik, The limit shape for convex lattice polygons and related topics, Funktsional Anal. i Prilozhen. 28(1) (1994), 16-25 (in Russian). English translation in Functional Anal. Appl. 28 (1994), 13-20.
12. A. M. Vershik, The limit shape for convex lattice polygons and related topics, Funktsional Anal. i Prilozhen. 28(1) (1994), 16-25 (in Russian). English translation in Functional Anal. Appl. 28 (1994), 13-20.