Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series A, Pt. 3, 337--346

Van den BERG-KESTEN INEQUALITY FOR THE POISSON BOOLEAN MODEL FOR CONTINUUM PERCOLATION

By

J.C. GUPTA,

and

B.V. RAO, Indian Statistical Institute, Calcutta

SUMMARY. For the Poisson Boolean model of continuum percolation we prove the Van den Berg-Kesten inequality >I>P (A \stackrel{\fbox{}}{} B ) <= P(A)P(B) for any two events A and B living on a bounded region.

AMS (1991) subject classification. 60K35, 82B43.

Key words and phrases. Poisson Boolean model, continuum percolation, Van den Berg-Kesten inequality.

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