Real zeros of random algebraic polynomials with binomial elements
نویسندگان
چکیده
منابع مشابه
Real Zeros of Random Algebraic Polynomials with Binomial Elements
This paper provides an asymptotic estimate for the expected number of real zeros of a random algebraic polynomial a0 + a1x + a2x + ···+ an−1xn−1. The coefficients aj ( j = 0,1,2, . . . ,n− 1) are assumed to be independent normal random variables withmean zero. For integers m and k = O(logn)2 the variances of the coefficients are assumed to have nonidentical value var(aj) = ( k−1 j−ik ) , where ...
متن کاملReal 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 ...
متن کاملAlgebraic Polynomials with Random Coefficients with Binomial and Geometric Progressions
The expected number of real zeros of an algebraic polynomial ao a1x a2x · · · anx with random coefficient aj , j 0, 1, 2, . . . , n is known. The distribution of the coefficients is often assumed to be identical albeit allowed to have different classes of distributions. For the nonidentical case, there has been much interest where the variance of the jth coefficient is var aj ( n j ) . It is sh...
متن کاملReal Almost Zeros of Random Polynomials with Complex Coefficients
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...
متن کاملExpected Discrepancy for Zeros of Random Algebraic Polynomials
We study asymptotic clustering of zeros of random polynomials, and show that the expected discrepancy of roots of a polynomial of degree n, with not necessarily independent coefficients, decays like √ logn/n. Our proofs rely on discrepancy results for deterministic polynomials, and order statistics of a random variable. We also consider the expected number of zeros lying in certain subsets of t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Applied Mathematics and Stochastic Analysis
سال: 2006
ISSN: 1048-9533,1687-2177
DOI: 10.1155/jamsa/2006/13980