Zeros of polynomials with random coefficients
نویسندگان
چکیده
منابع مشابه
Real Zeros of Algebraic Polynomials with Dependent Random Coefficients
The expected number of real zeros of polynomials a0+a1x+a2x+ · · · + an−1xn−1 with random coefficients is well studied. For n large and for the normal zero mean independent coefficients, irrespective of the distribution of coefficients, this expected number is known to be asymptotic to (2/π) logn. For the dependent cases studied so far it is shown that this asymptotic value remains O(logn). In ...
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We present a simple formula for the expected number of times that a complex-valued Gaussian stochastic process has a zero imaginary part and the absolute value of its real part is bounded by a constant value M. We show that only some mild conditions on the stochastic process are needed for our formula to remain valid. We further apply this formula to a random algebraic polynomial with complex c...
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For a regular compact set K in C and a measure μ on K satisfying the Bernstein-Markov inequality, we consider the ensemble PN of polynomials of degree N , endowed with the Gaussian probability measure induced by L(μ). We show that for large N , the simultaneous zeros of m polynomials in PN tend to concentrate around the Silov boundary of K; more precisely, their expected distribution is asympto...
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k−point correlations of complex zeros for Gaussian ensembles of Random Polynomials of order N with Real Coefficients (GRPRC) are calculated exactly, following an approach of Hannay [5] for the case of Gaussian Random Polynomials with Complex Coefficients (GRPCC). It is shown that in the thermodynamic limit N → ∞ of Gaussian random holomorphic functions all the statistics converge to the their G...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2015
ISSN: 0021-9045
DOI: 10.1016/j.jat.2014.09.003