Consider the polynomial $p(z)=\sum_0^na_iz^k$ where $a_n=1$ and $a_k \sim N(0,1),k=0,1,2,n-1.$ What is the probability that 2 will a bound of the roots of the polynomial?How can we find the asymptotic probability for the same?I did a simulation for a polynomial of this type of degree 5 and I found almost 91% of the cases ,the roots lies within $|z| \leq 2.$However,i do not know how to go about it anlytically .I would be delighted and highly obliged for any help\hints\references
2026-04-02 11:45:12.1775130312
probability of a number being a bound
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