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9 - Probabilistic Methods

Published online by Cambridge University Press:  21 April 2021

Tom Leinster
Affiliation:
University of Edinburgh
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Summary

Probability theory can be used to solve certain entirely deterministic functional equations, using a technique pioneered by Aubrun and Nechita. We give some background on moment generating functions, large deviations, and convex conjugates, then state Aubrun and Nechita’s multiplicative characterization of the p-norms (giving a variant of their proof). We then use this theorem on norms to give a multiplicative characterization of the power means.

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Entropy and Diversity
The Axiomatic Approach
, pp. 303 - 328
Publisher: Cambridge University Press
Print publication year: 2021

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  • Probabilistic Methods
  • Tom Leinster, University of Edinburgh
  • Book: Entropy and Diversity
  • Online publication: 21 April 2021
  • Chapter DOI: https://doi.org/10.1017/9781108963558.011
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  • Probabilistic Methods
  • Tom Leinster, University of Edinburgh
  • Book: Entropy and Diversity
  • Online publication: 21 April 2021
  • Chapter DOI: https://doi.org/10.1017/9781108963558.011
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Probabilistic Methods
  • Tom Leinster, University of Edinburgh
  • Book: Entropy and Diversity
  • Online publication: 21 April 2021
  • Chapter DOI: https://doi.org/10.1017/9781108963558.011
Available formats
×