Hafnians, perfect matchings and Gaussian matrices

@inproceedings{Rudelson2014HafniansPM,
  title={Hafnians, perfect matchings and Gaussian matrices},
  author={Mark Rudelson and Alex Samorodnitsky and Ofer Zeitouni},
  year={2014}
}
We analyze the behavior of the Barvinok estimator of the hafnian of even dimension, symmetric matrices with non negative entries. We introduce a condition under which the Barvinok estimator achieves sub-exponential 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… CONTINUE READING
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