Limit theory for planar gilbert tessellations

Probability and Mathematical Statistics

Volumn 31, Issue 1, 2011, Pages 149-160

  Schreiber, Tomasz ^a   Soja, Natalia ^a  

^a NICOLAUS COPERNICUS UNIVERSITY   (Poland)

Author keywords

Central limit theorem; Gilbert crack tessellation; Law of large numbers; Stabilizing geometric functionals

Indexed keywords

EID: 79960753744     PISSN: 02084147     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. Yu. Baryshnikov and J. E. Yukich, Gaussian limits for random measures in geometric probability, Ann. Appl. Probab. 15, 1A (2005), pp. 213-253.
2. S. N. Chiu, A central limit theorem for linear Kolmogorov's birth-growth models, Stochastic Process. Appl. 66 (1997), pp. 97-106.
3. S. N. Chiu and H. Y. Lee, A regularity condition and strong limit theorems for linear birth-growth processes, Math. Nachr. 241 (2002), pp. 21-27.
4. S. N. Chiu and M. P. Quine, Central limit theory for the number of seeds in a growth model in Rd with inhomogeneous Poisson arrivals, Ann. Appl. Probab. 7 (1997), pp. 802-814.
5. S. N. Chiu and M. P. Quine, Central limit theorem for germination-growth models in Rd with non-Poisson locations, Adv. in Appl. Probab. 33 (2001), pp. 751-755.
6. C. Cotar and S. Volkov, A note on the lilypond model, Adv. in Appl. Probab. 36 (2004), pp. 325-339.
7. D. J. Daley and G. Last, Descending chains, the lilypond model and mutual-nearestneighbour matching, Adv. in Appl. Probab. 37 (2005), pp. 604-628.
8. N. H. Gray, J. B. Anderson, J. D. Devine and J. M. Kwasnik, Topological properties of random crack networks, Math. Geol. 8 (1976), pp. 617-626.
9. O. Haeggstroem and R. Meester, Nearest neighbour and hard sphere models in continuum percolation, Random Structures and Algorithms 9 (1996), pp. 295-315.
10. M. Heveling and G. Last, Existence, uniqueness, and algorithmics computation of general lilypond systems, Random Structures and Algorithms 29 (2006), pp. 338-350.
11. L. Holst, M. P. Quine and J. Robinson, A general stochastic model for nucleation and linear growth, Ann. Appl. Probab. 6 (1996), pp. 903-921.
12. M. S. Makisack and R. E. Miles, Homogeneous rectangular tessellations, Adv. in Appl. Probab. 28 (1996), pp. 993-1013.
13. L. Muche and D. Stoyan, Contact and chord length distributions of the Poisson Voronoi tessellation, J. Appl. Probab. 29 (1992), pp. 467-471.
14. M. D. Penrose, Gaussian limits for random geometric measures, European Journal of Probability 12 (2007), pp. 989-1035.
15. M. D. Penrose, Laws of large numbers in stochastic geometry with statistical applications, Bernoulli 13 (2007), pp. 1124-1150.
16. M. D. Penrose and J. E. Yukich, Central limit theorems for some graphs in computational geometry, Ann. Appl. Probab. 11 (2001), pp. 1005-1041.
17. M. D. Penrose and J. E. Yukich, Limit theory for random sequential packing and deposition, Ann. Appl. Probab. 12 (2002), pp. 272-301.
18. M. D. Penrose and J. E. Yukich, Weak laws of large numbers in geometric probability, Ann. Appl. Probab. 13 (2004), pp. 277-303.
19. M. D. Penrose and J. E. Yukich, Normal approximation in geometric probability, in: Stein's Method and Applications, A. D. Barbour and Louis H. Y. Chen (Eds.), Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, Vol. 5 (2005), pp. 37-58.
20. T. Schreiber, Limit theorems in stochastic geometry, in: New Perspectives in Stochastic Geometry, W. S. Kendall and I. Molchanov (Eds.), Oxford University Press, 2009, pp. 111-144.
21. D. Stoyan, W. Kendall and J. Mecke, Stochastic Geometry and Its Applications, second edition, Wiley, Chichester 1995.