Low-Degree Approximation of Random Polynomials
Low-Degree Approximation of Random Polynomials
Abstract We prove that with “high probability” a random Kostlan polynomial in $$n+1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> many variables and of degree d can be approximated by a polynomial of “low degree” without changing the topology of its zero set on the sphere $$\mathbb {S}^n$$ <mml:math …