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The notion of the capacity of a polynomial was introduced by Gurvits around 2005, originally to give drastically simplified proofs of the Van der Waerden lower bound for permanents of doubly stochastic matrices and Schrijver's inequality for perfect matchings of regular bipartite graphs.
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Leonid Gurvits, Hyperbolic polynomials approach to Van der Waerden/Schrijver-Valiant like conjectures: sharper bounds, simpler proofs and algorithmic applications , Proceedings of the thirty-eighth annual ACM symposium on Theory of computing, ACM, 2006, pp. 417–426
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James Renegar, Hyperbolic programs, and their derivative relaxations , Foundations of Computational Mathematics 6
2006
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Petter Brändén, Polynomials with the half-plane property and matroid theory , Advances in Mathematics 216
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Shmuel Friedland and Leonid Gurvits, Lower bounds for partial matchings in regular bipartite graphs and applications to the monomer–dimer entropy , Combinatorics, Probability and Computing 17
2008
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2009
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2017
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2017
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Damian Straszak and Nisheeth K. Vishnoi, Real stable polynomials and matroids: Optimization and counting , Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, ACM, 2017, pp. 370–383
2017
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Samuel Zackrisson, Coefficients and zeros of mixed characteristic polynomials , 2017
2017
Later among the works it cites.
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2014
Cited alongside, same era.
2015
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2015
Cited alongside, same era.
Nima Anari and Shayan Oveis Gharan, A generalization of permanent inequalities and applications in counting and optimization , Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, ACM, 2017, pp. 384–396
2017
Cited alongside, same era.
2018
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Karim Adiprasito, June Huh, and Eric Katz, Hodge theory for combinatorial geometries , Annals of Mathematics 188
2018
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2018
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