Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Percolation of level sets for two-dimensional random fields with lattice symmetry

Percolation of level sets for two-dimensional random fields with lattice symmetry Let ψ(x),x∈ℝ2, be a random field, which may be viewed as the potential of an incompressible flow for which the trajectories follow the level lines of ψ. Percolation methods are used to analyze the sizes of the connected components of level sets {x:ψ(x)=h} and sets {x:ψ(x)≦h} in several classes of random fields with lattice symmetry. In typical cases there is a sharp transition at a critical value ofh from exponential boundedness for such components to the existence of an unbounded component. In some examples, however, there is a nondegenerate interval of values ofh where components are bounded but not exponentially so, and in other cases each level set may be a single infinite line which visits every region of the lattice. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Statistical Physics Springer Journals

Percolation of level sets for two-dimensional random fields with lattice symmetry

Loading next page...
 
/lp/springer-journals/percolation-of-level-sets-for-two-dimensional-random-fields-with-O6LdRsHPEO

References (23)

Publisher
Springer Journals
Copyright
Copyright
Subject
Physics; Statistical Physics and Dynamical Systems; Theoretical, Mathematical and Computational Physics; Physical Chemistry; Quantum Physics
ISSN
0022-4715
eISSN
1572-9613
DOI
10.1007/BF02179453
Publisher site
See Article on Publisher Site

Abstract

Let ψ(x),x∈ℝ2, be a random field, which may be viewed as the potential of an incompressible flow for which the trajectories follow the level lines of ψ. Percolation methods are used to analyze the sizes of the connected components of level sets {x:ψ(x)=h} and sets {x:ψ(x)≦h} in several classes of random fields with lattice symmetry. In typical cases there is a sharp transition at a critical value ofh from exponential boundedness for such components to the existence of an unbounded component. In some examples, however, there is a nondegenerate interval of values ofh where components are bounded but not exponentially so, and in other cases each level set may be a single infinite line which visits every region of the lattice.

Journal

Journal of Statistical PhysicsSpringer Journals

Published: Sep 2, 2005

There are no references for this article.