On the expected number of real roots of a system of random polynomial equations
On the expected number of real roots of a system of random polynomial equations
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关于随机多项式方程组的期望实根数
DOI：
10.1142/9789812778031_0007
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发表时间：
2002
影响因子：
3
通讯作者：
E. Kostlan
中科院分区：
文献类型：
--
作者：
E. Kostlan
统一和推广了关于随机多项式系统的几个已知结果。本文首先对多项式映射空间的正交不变正规测度进行了分类。对于每一个这样的措施，我们计算期望的真实的零的数量。不变措施的结果扩展到欠定系统，正交不变的随机真实的投影品种的预期量。然后，我们考虑非不变的措施，并显示如何随机多项式的真实的零点的行为下直和，张量积和组合。
We unify and generalize several known results about systems of random polynomials. We first classify all orthogonally invariant normal measures for spaces of polynomial mappings. For each such measure we calculate the expected number of real zeros. The results for invariant measures extend to underdetermined systems, giving the expected volume for orthogonally invariant random real projective varieties. We then consider noninvariant measures, and show how the real zeros of random polynomials behave under direct sum, tensor product and composition.