EXPONENTIAL OF THE S1 TRACE OF THE FREE FIELD AND VERBLUNSKY COEFFICIENTS

Mohammad Javad Latifi, Doug Pickrell

Research output: Contribution to journalArticlepeer-review

Abstract

An identity of Szego, and a volume calculation, heuristically suggest a simple expression for the distribution of Verblunsky coefficients with respect to the (normalized) exponential of the S1 trace of the Gaussian free field. This heuristic expression is not quite correct. A proof of the correct formula has been found by Chhaibi and Najnudel (2019). Their proof uses random matrix theory and overcomes many difficult technical issues. In addition to presenting the Szego perspective, we show that the Chhaibi and Najnudel theorem implies a family of combinatorial identities (for moments of measures) which are of intrinsic interest.

Original languageEnglish (US)
Pages (from-to)899-924
Number of pages26
JournalRocky Mountain Journal of Mathematics
Volume52
Issue number3
DOIs
StatePublished - Jun 2022

Keywords

  • Gaussian free field
  • Loop group factorization
  • Verblunsky coefficients

ASJC Scopus subject areas

  • Mathematics(all)

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