The local geometry of finite mixtures

Elisabeth Gassiat, Ramon Van Handel

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We establish that for q ≥ 1, the class of convex combinations of q translates of a smooth probability density has local doubling dimension proportional to q. The key difficulty in the proof is to control the local geometric structure of mixture classes. Our local geometry theorem yields a bound on the (bracketing) metric entropy of a class of normalized densities, from which a local entropy bound is deduced by a general slicing procedure.

Original languageEnglish (US)
Pages (from-to)1047-1072
Number of pages26
JournalTransactions of the American Mathematical Society
Issue number2
StatePublished - 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


  • Bracketing numbers
  • Finite mixtures
  • Local metric entropy


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