The polaron measure

Chiranjib Mukherjee, S. R.S. Varadhan

Research output: Chapter in Book/Report/Conference proceedingChapter


{x(t) − x(s)} are the increments of the three dimensional Brownian motion over the intervals [s, t]. (Formula Presented). Qα,T is defined as the measure with Radon–Nikodym derivative [Z(T, α)]−1 exp [αF(T, ω)] with respect to Brownian Motion, Z(α, T) being the normalization constant Z(T, α) = E[exp [αF(T, ω)]]. We are interested in the existence of the Polaron measure Qα =limT→∞Qα,T, the validity of central limit theorem for (Formula Presented) under Qα,T as well as Qα and the behavior of Qα for large α.

Original languageEnglish (US)
Title of host publicationInfosys Science Foundation Series in Mathematical Sciences
Number of pages5
StatePublished - 2020

Publication series

NameInfosys Science Foundation Series in Mathematical Sciences
ISSN (Print)2364-4036
ISSN (Electronic)2364-4044


  • Birth death process
  • Gaussian process
  • Polaron measure
  • Regeneration property
  • White noise

ASJC Scopus subject areas

  • General Mathematics


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