Arbitrarily slow approach to limiting behavior

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Publication Type Journal Article
School or College College of Science
Department Mathematics
Creator Golden, Kenneth M.
Other Author Goldstein, S.
Title Arbitrarily slow approach to limiting behavior
Date 1991
Description ABSTRACT. Let f(k, t): RN x [0, oo) -- R be jointly continuous in k and t, with lim(t)--(oo) f(k, t) = F(k) discontinuous for a dense set of k's. It is proven that there exists a dense set T of k's such that, for k e T , |f(k, t) - F(k)| approaches 0 arbitrarily slowly, i.e., roughly speaking, more slowly than any expressible function g(t) -- 0 . This result is applied to diffusion and conduction in quasiperiodic media and yields arbitrarily slow approaches to limiting behavior as time or volume becomes infinite. Such a slow approach is in marked contrast to the power laws widely found for random media, and, in fact, implies that there is no law whatsoever governing the asymptotics.
Type Text
Publisher American Mathematical Society (AMS)
Volume 112
Issue 1
First Page 109
Last Page 119
Subject Random; Conductivity; Diffusion
Language eng
Bibliographic Citation Golden, K. M., & Goldstein S. (1991). Arbitrarily slow approach to limiting behavior. Proceedings of the American Mathematical Society, 112(1), 109-19.
Rights Management (c) American Mathematical Society
Format Medium application/pdf
Format Extent 3,175,057 bytes
Identifier ir-main,5726
ARK ark:/87278/s6v41cvs
Setname ir_uspace
Date Created 2012-06-13
Date Modified 2012-06-13
ID 707464
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