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Limit theorems for monotonic particle systems and sequential deposition

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  • Penrose, Mathew D.

Abstract

We prove spatial laws of large numbers and central limit theorems for the ultimate number of adsorbed particles in a large class of multidimensional random and cooperative sequential adsorption schemes on the lattice, and also for the Johnson-Mehl model of birth, linear growth and spatial exclusion in the continuum. The lattice result is also applicable to certain telecommunications networks. The proofs are based on a general law of large numbers and central limit theorem for sums of random variables determined by the restriction of a white noise process to large spatial regions.

Suggested Citation

  • Penrose, Mathew D., 2002. "Limit theorems for monotonic particle systems and sequential deposition," Stochastic Processes and their Applications, Elsevier, vol. 98(2), pages 175-197, April.
    • Handle: RePEc:eee:spapps:v:98:y:2002:i:2:p:175-197
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    Cited by:

    1. Penrose, Mathew D. & Rosoman, Tom, 2012. "Percolation of even sites for random sequential adsorption," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1866-1886.
    2. Daniels, Christopher J.E. & Penrose, Mathew D., 2017. "Percolation of even sites for enhanced random sequential adsorption," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 803-830.

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