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Volumn 29, Issue 4, 2001, Pages 1515-1546

A central limit theorem with applications to percolation, epidemics and boolean models

Author keywords

Boolean model; Central limit theorem; Geometric probability; Martingale; Percolation

Indexed keywords


EID: 0035470870     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1015345760     Document Type: Article
Times cited : (25)

References (34)
  • 1
    • 0031222111 scopus 로고    scopus 로고
    • Limit theorems for the total size of a spatial epidemic
    • ANDERSSON, H. and DJEHICHE, B. (1997). Limit theorems for the total size of a spatial epidemic. J. Appl. Probab. 34 698-710.
    • (1997) J. Appl. Probab. , vol.34 , pp. 698-710
    • Andersson, H.1    Djehiche, B.2
  • 2
    • 0000380180 scopus 로고
    • On central limit theorems in geometrical probability
    • AVRAM, F. and BERTSIMAS, D. (1993). On central limit theorems in geometrical probability. Ann. Appl. Probab. 3 1033-1046.
    • (1993) Ann. Appl. Probab. , vol.3 , pp. 1033-1046
    • Avram, F.1    Bertsimas, D.2
  • 4
    • 0000791029 scopus 로고
    • Limit theorems for the spread of epidemics and forest fires
    • COX, J. T. and DURRETT, R. (1988). Limit theorems for the spread of epidemics and forest fires. Stochastic Processes Appl. 30 171-191.
    • (1988) Stochastic Processes Appl. , vol.30 , pp. 171-191
    • Cox, J.T.1    Durrett, R.2
  • 10
    • 0001626028 scopus 로고
    • The supercritical phase of percolation is well behaved
    • GRIMMETT, G. and MARSTRAND, J. M. (1990). The supercritical phase of percolation is well behaved. Proc. Roy. Soc. London Ser. A 430 439-457.
    • (1990) Proc. Roy. Soc. London Ser. A , vol.430 , pp. 439-457
    • Grimmett, G.1    Marstrand, J.M.2
  • 11
    • 51249172134 scopus 로고
    • Distribution of size, structure and number of vacant regions in a high-intensity mosaic
    • HALL, P. (1985). Distribution of size, structure and number of vacant regions in a high-intensity mosaic. Z. Warsch. Verw. Gebiete 70 237-261.
    • (1985) Z. Warsch. Verw. Gebiete , vol.70 , pp. 237-261
    • Hall, P.1
  • 12
    • 0007258644 scopus 로고
    • Clump counts in a mosaic
    • HALL, P. (1986). Clump counts in a mosaic. Ann. Probab. 14 424-458.
    • (1986) Ann. Probab. , vol.14 , pp. 424-458
    • Hall, P.1
  • 14
    • 0033141155 scopus 로고    scopus 로고
    • Central limit theorem for a class of random measures associated with germ-grain models
    • HEINRICH, L. and MOLCHANOV, I. S. (1999). Central limit theorem for a class of random measures associated with germ-grain models. Adv. Appl. Probab. 31 283-314.
    • (1999) Adv. Appl. Probab. , vol.31 , pp. 283-314
    • Heinrich, L.1    Molchanov, I.S.2
  • 16
    • 0030501338 scopus 로고    scopus 로고
    • The central limit theorem for weighted minimal spanning trees on random points
    • KESTEN, H. and LEE, S. (1996). The central limit theorem for weighted minimal spanning trees on random points. Ann. Appl. Probab. 6 495-527.
    • (1996) Ann. Appl. Probab. , vol.6 , pp. 495-527
    • Kesten, H.1    Lee, S.2
  • 17
    • 0031074947 scopus 로고    scopus 로고
    • A central limit theorem for critical first passage percolation in two dimensions
    • KESTEN, H. and ZHANG, Y. (1997). A central limit theorem for critical first passage percolation in two dimensions. Probab. Theory Related Fields 107 137-160.
    • (1997) Probab. Theory Related Fields , vol.107 , pp. 137-160
    • Kesten, H.1    Zhang, Y.2
  • 18
    • 0031260688 scopus 로고    scopus 로고
    • The central limit theorem for Euclidean minimal spanning trees I
    • LEE, S. (1997) The central limit theorem for Euclidean minimal spanning trees I. Ann. Appl. Probab. 7 996-1020
    • (1997) Ann. Appl. Probab. , vol.7 , pp. 996-1020
    • Lee, S.1
  • 20
    • 0000618154 scopus 로고
    • Symmetric sampling procedures, general epidemic processes and their threshold limit theorems
    • MARTIN-LÖF, A. (1986). Symmetric sampling procedures, general epidemic processes and their threshold limit theorems. J. Appl. Probab. 23 265-282.
    • (1986) J. Appl. Probab. , vol.23 , pp. 265-282
    • Martin-Löf, A.1
  • 22
    • 0000964674 scopus 로고
    • Dependent central limit theorems and invariance principles
    • MCLEISH, D. L. (1974). Dependent central limit theorems and invariance principles. Ann. Probab. 2 620-628.
    • (1974) Ann. Probab. , vol.2 , pp. 620-628
    • McLeish, D.L.1
  • 24
    • 0032397960 scopus 로고    scopus 로고
    • Consistent estimation of percolation quantities
    • MEESTER, R. and STEIF, J. (1998). Consistent estimation of percolation quantities. Statist Neerlandica 52 226-238.
    • (1998) Statist Neerlandica , vol.52 , pp. 226-238
    • Meester, R.1    Steif, J.2
  • 26
    • 0007259921 scopus 로고    scopus 로고
    • A limit theorem for scaled vacancies of the Boolean model
    • MOLCHANOV, I. (1998). A limit theorem for scaled vacancies of the Boolean model. Stochastics Stochastics Rep. 58 45-65.
    • (1998) Stochastics Stochastics Rep. , vol.58 , pp. 45-65
    • Molchanov, I.1
  • 27
    • 0035497809 scopus 로고    scopus 로고
    • Central limit theorems for some graphs in computational geometry
    • PENROSE, M. D. and YUKICH, J. E. (2001) Central limit theorems for some graphs in computational geometry. Ann. Appl Probab. 11 1005-1041.
    • (2001) Ann. Appl Probab. , vol.11 , pp. 1005-1041
    • Penrose, M.D.1    Yukich, J.E.2
  • 28
    • 0007262590 scopus 로고    scopus 로고
    • Large deviations for discrete and continuous percolation
    • PENROSE, M. D. and PISZTORA, A. (1996). Large deviations for discrete and continuous percolation. Adv. Appl. Probab. 28 29-52.
    • (1996) Adv. Appl. Probab. , vol.28 , pp. 29-52
    • Penrose, M.D.1    Pisztora, A.2
  • 29
    • 0042416901 scopus 로고    scopus 로고
    • Surface order large deviations for ising, potts and percolation models
    • PISZTORA, A. (1996) Surface order large deviations for Ising, Potts and Percolation models. Probab. Theory Related Fields 104 427-466.
    • (1996) Probab. Theory Related Fields , vol.104 , pp. 427-466
    • Pisztora, A.1
  • 30
    • 0007267908 scopus 로고
    • Percolation of poisson sticks on the plane
    • ROY, R. (1991). Percolation of Poisson sticks on the plane. Probab. Theory Related Fields 89 503-517.
    • (1991) Probab. Theory Related Fields , vol.89 , pp. 503-517
    • Roy, R.1


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