Greven A (1990)
Publication Language: English
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 1990
Publisher: Springer Verlag (Germany)
Book Volume: 85
Pages Range: 307-364
Journal Issue: 3
DOI: 10.1007/BF01193942
We study symmetric exclusion on a random set, where the underlying kernel p(x, y) is strictly positive. The random set is generated by Bernoulli experiments with success probability q. We prove that for certain values of the involved parameters the transport of particles through the system is drastically different from the classical situation on ℤ. In dimension one and {Mathematical expression} the transport of particles occurs on a nonclassical scale and is (on a macroscopic scale)not governed by the heat equation as in the case:r<|log(1-q)| on a random set, or in the classical situation on ℤ. The reason for this behaviour is, that a random walk with jump rates p(x, y) restricted to the random set, converges to Brownian motion in the usual scaling if r<|log(1-q)| but yields nontrivial limit behaviour only in the scaling x→ux,t→ut(α>) if + ∞ >r > |log(1-q)|. We calculate α and study the limiting processes for the various scalings for fixed random sets. We shortly discuss the case r=+∞, here in general a great variety of scales yields nontrivial limits. Finally we discuss the case of a "stationary" random set. © 1990 Springer-Verlag.
APA:
Greven, A. (1990). Symmetric exclusion on random sets and a related problem for random walks in random environment. Probability Theory and Related Fields, 85(3), 307-364. https://dx.doi.org/10.1007/BF01193942
MLA:
Greven, Andreas. "Symmetric exclusion on random sets and a related problem for random walks in random environment." Probability Theory and Related Fields 85.3 (1990): 307-364.
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