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Majorizing Measures, Codes, and Information
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DOI：10.1109/tit.2026.3673035.png)
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Abstract
En 中文
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.
Keywords:
Codes
Measurement
Information theory
Upper bound
Random processes
Gaussian processes
Extraterrestrial measurements
Finite element analysis
Lower bound
Trees (botanical)
Majorizing measures
stochastic processes
variable-length codes on metric spaces
Journal
I
IF:
2.9
Papers:
317
Citations:
0
