Expected number of real zeros for random linear combinations of orthogonal polynomials
نویسندگان
چکیده
منابع مشابه
Expected Number of Real Zeros for Random Linear Combinations of Orthogonal Polynomials
We study the expected number of real zeros for random linear combinations of orthogonal polynomials. It is well known that Kac polynomials, spanned by monomials with i.i.d. Gaussian coefficients, have only (2/π + o(1)) logn expected real zeros in terms of the degree n. On the other hand, if the basis is given by Legendre (or more generally by Jacobi) polynomials, then random linear combinations...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2015
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/12836