Deterministic Approximations of Random Reflectors
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Sheffield_Deterministic approximations.pdf
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269.16 KB
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Adobe PDF
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301e9fed152dd268926aaae76ca8ca7a
Author(s)
Sheffield, Scott Roger
Date Issued
June 2013
Journal
Transactions of the American Mathematical Society
Publisher
American Mathematical Society (AMS)
Citation
Angel, Omer, Krysztof Burdzy, and Scott Sheffield. "Deterministic Approximations of Random Reflectors." Trans. Amer. Math. Soc. 365 (2013): 6367-6383. © 2013 American Mathematical Society
Version
Final published version
Abstract
Within classical optics, one may add microscopic "roughness'' to a macroscopically flat mirror so that parallel rays of a given angle are reflected at different outgoing angles. Taking the limit (as the roughness becomes increasingly microscopic) one obtains a flat surface that reflects randomly, i.e., the transition from incoming to outgoing ray is described by a probability kernel (whose form depends on the nature of the microscopic roughness).
We consider two-dimensional optics (a.k.a. billiards) and show that every random reflector on a line that satisfies a necessary measure-preservation condition (well established in the theory of billiards) can be approximated by deterministic reflectors in this way.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
http://www.ams.org/journals/tran/2013-365-12/S0002-9947-2013-05851-5/
