Majorizing Measures, Codes, and Information

Yifeng Chu; Maxim Raginsky

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arXiv · 2305.02960

Majorizing Measures, Codes, and Information

Yifeng Chu·Maxim Raginsky

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Abstract

The majorizing measure theorem of Fernique and Talagrand is a fundamental result in the theory of random processes. It relates the boundedness of random processes indexed by elements of a metric space to complexity measures arising from certain multiscale combinatorial structures, such as packing and covering trees. This paper builds on the ideas first outlined in a little-noticed preprint of Andreas Maurer to present an information-theoretic perspective on the majorizing measure theorem, according to which the boundedness of random processes is phrased in terms of the existence of efficient variable-length codes for the elements of the indexing metric space.

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Yifeng Chu, Maxim Raginsky. 2023-05-04. Majorizing Measures, Codes, and Information. https://arxiv.org/abs/2305.02960

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