Coverage of the whole space

Reference:

Shcherbakov, V. and Molchanov, I., 2003. Coverage of the whole space. Advances in Applied Probability, 35, 898--912.

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Abstract

Consider an inhomogeneous germ-grain model with spherical grains whose radii depend on their positions through a rate function, possibly perturbed by a random noise. We find the critical rate function that separates the cases when the germ-grain model covers the whole space with a positive probability and when the total coverage occurs with probability zero.

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