The Annals of Probability

Hafnians, perfect matchings and Gaussian matrices

Mark Rudelson, Alex Samorodnitsky, and Ofer Zeitouni

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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.

Article information

Source
Ann. Probab., Volume 44, Number 4 (2016), 2858-2888.

Dates
Received: September 2014
Revised: June 2015
First available in Project Euclid: 2 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.aop/1470139156

Digital Object Identifier
doi:10.1214/15-AOP1036

Mathematical Reviews number (MathSciNet)
MR3531682

Zentralblatt MATH identifier
06631786

Subjects
Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 15B52: Random matrices
Secondary: 05C70: Factorization, matching, partitioning, covering and packing

Keywords
Hafnian perfect matching random Gaussian matrices

Citation

Rudelson, Mark; Samorodnitsky, Alex; Zeitouni, Ofer. Hafnians, perfect matchings and Gaussian matrices. Ann. Probab. 44 (2016), no. 4, 2858--2888. doi:10.1214/15-AOP1036. https://projecteuclid.org/euclid.aop/1470139156


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References

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