On roots of random polynomials
On roots of random polynomials
We study the distribution of the complex roots of random polynomials of degree <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with i.i.d. coefficients. Using techniques related to Riceās treatment of the real roots question, we derive, under appropriate moment and regularity conditions, an exact formula ā¦