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Computing the distribution of permanents of random matrices has been an outstanding open problem for several decades.
“The distribution of random determinants”
Harry Nyquist, SO Rice and J Riordan · 1954
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“The complexity of computing the permanent”
Leslie Valiant · 1979
Earlier work this paper cites.
“The central limit theorem for random determinants”
Vyacheslav Girko · 1980
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“Random permanents and symmetric statistics”
Yuri Borovskikh and Vladimir Korolyuk · 1994
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“On the limit distribution of random permanents”
GJ Szekely and L Szeidl · 1995
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“Perspectives on invariant theory: Schur duality, multiplicity-free actions and beyond”
Roger Howe · 1995
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“Large Deviations Techniques and Applications”
A Dembod, O Zeltouni and K Fleischmann · 1996
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“Young tableaux: with applications to representation theory and geometry”
Mr Fulton and William Fulton · 1997
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“Limiting behavior of random permanents”
Grzegorz Rempala and Jacek Wesolowski · 1999
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“Lie groups”
Daniel Bump · 2004
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“Integration with respect to the Haar measure on unitary, orthogonal and symplectic group”
Benoit Collins and Piotr Sniady · 2006
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“On random ± \pm 1 matrices: singularity and determinant”
Terence Tao and Van Vu · 2006
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“On the permanent of random Bernoulli matrices”
Terence Tao and Van Vu · 2009
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“Symmetry, representations, and invariants”
Roe Goodman and Nolan Wallach · 2009
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“The computational complexity of linear optics”
“Theory of random determinants”
Viacheslav Girko · 2012
Later among the works it cites.
“Representation theory: a first course”
William Fulton and Joe Harris · 2013
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“Random matrices: Law of the determinant”
Hoi Nguyen and Van Vu · 2014
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“Recent developments on the moment problem”
Gwo Lin · 2017
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“Approximating Permanent of Random Matrices with Vanishing Mean: Made Better and Simpler”
Zhengfeng Ji, Zhihan Jin and Pinyan Lu · 2019
Later among the works it cites.
“Recent progress in combinatorial random matrix theory”
Van Vu · 2020
Later among the works it cites.
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Scott Aaronson and Alex Arkhipov · 2011
Cited alongside, same era.
“A basic introduction to large deviations: Theory, applications, simulations”
Hugo Touchette · 2011
Cited alongside, same era.
“Truncations of random unitary matrices”
Karol Zyczkowski and Hans-Jurgen Sommers · 2045
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