Polynomial averages in the Kontsevich model

P. Di Francesco, C. Itzykson, J. B. Zuber

Research output: Contribution to journalArticlepeer-review


We obtain in closed form averages of polynomials, taken over hermitian matrices with the Gaussian measure involved in the Kontsevich integral, and prove a conjecture of Witten enabling one to express analogous averages with the full (cubic potential) measure, as derivatives of the partition function with respect to traces of inverse odd powers of the external argument. The proofs are based on elementary algebraic identities involving a new set of invariant polynomials of the linear group, closely related to the general Schur functions.

Original languageEnglish (US)
Pages (from-to)193-219
Number of pages27
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - Jan 1993
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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