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A nucleation-and-growth model
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  • Published: January 1997

A nucleation-and-growth model

  • Pouria Dehghanpour1 &
  • Roberto H. Schonmann1 

Probability Theory and Related Fields volume 107, pages 123–135 (1997)Cite this article

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Summary.

We consider the following simple nucleation-and-growth model. On the lattice ℤ d, starting with all sites unoccupied, a site becomes occupied at rate e −ℬΓ if it has no occupied neighbors, at rate ɛ= e −βγ if it has 1 occupied neighbor, and at rate 1 if it has 2 or more occupied neighbors. Occupied sites remain occupied forever. The parameters Γ≧γ are fixed, and we are interested in the behavior of the system as β→∞. We show that the relaxation time of this system scales as e βκc, where κ c = max {γ,( Γ + γ)/(d+1)}.

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Authors and Affiliations

  1. Mathematics Department, University of California at Los Angeles, Los Angeles, CA 90095, USA (e-mail: rhs@ math.ucla.edu), , , , , , US

    Pouria Dehghanpour & Roberto H. Schonmann

Authors
  1. Pouria Dehghanpour
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  2. Roberto H. Schonmann
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Received: 20 February 1996 / In revised form: 15 June 1996

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Dehghanpour, P., Schonmann, R. A nucleation-and-growth model. Probab Theory Relat Fields 107, 123–135 (1997). https://doi.org/10.1007/s004400050079

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  • Issue Date: January 1997

  • DOI: https://doi.org/10.1007/s004400050079

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  • Mathematics Subject classification (1991):  60K35
  • 82A05
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