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2 results

  • 9 - Probabilistic Methods

  • Tom Leinster, University of Edinburgh
  • Book:
    Entropy and Diversity
    Published online:
    21 April 2021
    Print publication:
    22 April 2021, pp 303-328

  • 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.

  • AN Lp ‘COUSIN OF COBOUNDARY’ THEOREM FOR RANDOM FIELDS

  • Part of
  • RICHARD C. BRADLEY
  • Journal:
    Journal of the Australian Mathematical Society / Volume 85 / Issue 1 / August 2008
    Published online by Cambridge University Press:
    01 August 2008, pp. 51-58
    Print publication:
    August 2008
    • Article
      • You have access
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  • It is known that for a given and a given strictly stationary sequence of random variables, the p-norms of the partial sums are bounded if and only if the sequence consists of successive differences from another strictly stationary sequence with finite p-norm. Here this is generalized to random fields, and the assumption of stationarity is relaxed. The index is included.