Asymptotic variance of the number of real roots of random polynomial systems
نویسندگان
چکیده
منابع مشابه
On the Kostlan-Shub-Smale model for random polynomial systems. Variance of the number of roots
We consider a random polynomial system with m equations and m real unknowns. Assume all equations have the same degree d and the law on the coefficients satisfies the Kostlan-Shub-Smale hypotheses. It is known that E(N) = d where N denotes the number of roots of the system. Under the condition that d does not grow very fast, we prove that lim supm→+∞ V ar( N dm/2 ) ≤ 1. Moreover, if d ≥ 3 then ...
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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 v...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2018
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/14215