A Useful Renormalization Argument

  • Maury Bramson
  • Lawrence Gray
Part of the Progress in Probability book series (PRPR, volume 28)


We define a collection of ‘generic’ population models for which we prove a survival criterion by using a renormalization argument. These models can be compared with other more familiar models, leading to simple proofs of various survival results. In particular, we prove a generalization of Toom’s Theorem concerning survival in multidimensional probabilistic cellular automata. Our technique should also be applicable to a variety of other discrete and continuous time models.


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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Maury Bramson
    • 1
  • Lawrence Gray
    • 2
  1. 1.Dept. of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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