Hafnians, perfect matchings and Gaussian matrices

Mark Rudelson, Alex Samorodnitsky, Ofer Zeitouni

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We analyze the behavior of the Barvinok estimator of the hafnian of even dimension, symmetric matrices with nonnegative entries.We introduce a condition under which the Barvinok estimator achieves subexponential errors, and show that this condition is almost optimal. Using that hafnians count the number of perfect matchings in graphs, we conclude that Barvinok's estimator gives a polynomial-time algorithm for the approximate (up to subexponential errors) evaluation of the number of perfect matchings.

Original languageAmerican English
Pages (from-to)2858-2888
Number of pages31
JournalAnnals of Probability
Issue number4
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© Institute of Mathematical Statistics, 2016.


  • Hafnian
  • Perfect matching
  • Random Gaussian matrices


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