Fetching the paper…
Reading the bibliography…
We consider the zero sets $Z_N$ of systems of $m$ random polynomials of degree $N$ in $m$ complex variables, and we give asymptotic formulas for the random variables given by summing a smooth test function over $Z_N$.
M. Kac, On the average number of real roots of a random algebraic equation, II, Proc. London Math. Soc
1949
Earlier work this paper cites.
N. B. Maslova, The distribution of the number of real roots of random polynomials (Russian) Teor. Verojatnost. i Primenen
1974
Earlier work this paper cites.
G. Tian, On a set of polarized Kähler metrics on algebraic manifolds, J. Diff. Geometry
1990
Earlier work this paper cites.
M. Shub and S. Smale, Complexity of Bezout’s theorem. II. Volumes and probabilities, Computational algebraic geometry (Nice, 1992)
1993
Earlier work this paper cites.
A. Edelman and E. Kostlan, How many zeros of a random polynomial are real? Bull. Amer. Math. Soc
1995
Earlier work this paper cites.
E. Bogomolny, O. Bohigas, and P. Leboeuf, Quantum chaotic dynamics and random polynomials, J. Statist. Phys
1996
Earlier work this paper cites.
J. H. Hannay, Chaotic analytic zero points: exact statistics for those of a random spin state, J. Phys. A
1996
Earlier work this paper cites.
J. M. Rojas, On the average number of real roots of certain random sparse polynomial systems, The mathematics of numerical analysis (Park City, UT, 1995)
1996
Earlier work this paper cites.
P. Bleher and X. Di, Correlations between zeros of a random polynomial, J. Statist. Phys
1997
Cited alongside, same era.
S. Nonnenmacher and A. Voros, Chaotic eigenfunctions in phase space, J. Statist. Phys
1998
Cited alongside, same era.
S. Zelditch, Szegő kernels and a theorem of Tian, Internat. Math. Res. Notices
1998
Cited alongside, same era.
D. Catlin, The Bergman kernel and a theorem of Tian, in: Analysis and Geometry in Several Complex Variables
1999
Cited alongside, same era.
P. J. Forrester and G. Honner, Exact statistical properties of the zeros of complex random polynomials, J. Phys. A
1999
Cited alongside, same era.
B. Shiffman and S. Zelditch, Distribution of zeros of random and quantum chaotic sections of positive line bundles, Comm. Math. Phys
Q. Zhong, Energy of zeros of random sections on Riemann Surface, Indiana Univ. Math. J
2000
Later among the works it cites.
B. Shiffman and S. Zelditch, Asymptotics of almost holomorphic sections of ample line bundles on symplectic manifolds, J. Reine Angew. Math
2002
Later among the works it cites.
B. Shiffman and S. Zelditch, Equilibrium distribution of zeros of random polynomials, Int. Math. Res. Not
2003
Later among the works it cites.
M. Sodin and B. Tsirelson, Random complex zeros, I. Asymptotic normality, Israel J. Math
2004
Later among the works it cites.
T. Bloom, Random polynomials and Green functions, Int. Math. Res. Not
2005
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
1999
Cited alongside, same era.
P. Bleher, B. Shiffman and S. Zelditch, Poincaré-Lelong approach to universality and scaling of correlations between zeros, Comm. Math. Phys
2000
Cited alongside, same era.
P. Bleher, B. Shiffman and S. Zelditch, Universality and scaling of correlations between zeros on complex manifolds, Invent. Math
2000
Cited alongside, same era.
R. Berman, Bergman kernels and weighted equilibrium measures of ℂ n {\mathbb{C}}^{n} , preprint (arXiv:math/0702357)
Cited in the paper.
B. Shiffman, Convergence of random zeros on complex manifolds, preprint (arXiv:0708.2754)
Cited in the paper.
B. Shiffman and S. Zelditch, Number variance of random zeros on complex manifolds, Geom. Funct. Anal
Cited in the paper.
Cited in the paper.
M. Wschebor, On the Kostlan-Shub-Smale model for random polynomial systems. Variance of the number of roots, J. Complexity
2005
Later among the works it cites.
T. Bloom and B. Shiffman, Zeros of random polynomials on ℂ m {\mathbb{C}}^{m} , Math. Res. Lett
2007
Closest in time.