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July 2016 Hafnians, perfect matchings and Gaussian matrices
Mark Rudelson, Alex Samorodnitsky, Ofer Zeitouni
Ann. Probab. 44(4): 2858-2888 (July 2016). DOI: 10.1214/15-AOP1036

Abstract

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.

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Mark Rudelson. Alex Samorodnitsky. Ofer Zeitouni. "Hafnians, perfect matchings and Gaussian matrices." Ann. Probab. 44 (4) 2858 - 2888, July 2016. https://doi.org/10.1214/15-AOP1036

Information

Received: 1 September 2014; Revised: 1 June 2015; Published: July 2016
First available in Project Euclid: 2 August 2016

zbMATH: 06631786
MathSciNet: MR3531682
Digital Object Identifier: 10.1214/15-AOP1036

Subjects:
Primary: 15B52 , 60B20
Secondary: 05C70

Keywords: Hafnian , perfect matching , random Gaussian matrices

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 4 • July 2016
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