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2013 | OriginalPaper | Chapter

12. Probabilistic Frames: An Overview

Authors : Martin Ehler, Kasso A. Okoudjou

Published in: Finite Frames

Publisher: Birkhäuser Boston

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Abstract

Finite frames can be viewed as mass points distributed in N-dimensional Euclidean space. As such they form a subclass of a larger and rich class of probability measures that we call probabilistic frames. We derive the basic properties of probabilistic frames, and we characterize one of their subclasses in terms of minimizers of some appropriate potential function. In addition, we survey a range of areas where probabilistic frames, albeit under different names, appear. These areas include directional statistics, the geometry of convex bodies, and the theory of t-designs.

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previous chapter The Kadison–Singer and Paulsen Problems in Finite Frame Theory

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Title: Probabilistic Frames: An Overview
Authors: Martin Ehler
Kasso A. Okoudjou
Publisher: Birkhäuser Boston
Book: Finite Frames
Print ISBN: 978-0-8176-8372-6

Electronic ISBN: 978-0-8176-8373-3

Copyright Year: 2013
DOI: https://doi.org/10.1007/978-0-8176-8373-3_12

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