Abstract
The classical Markov polynomial inequality bounds the uniform norm of the derivative of a polynomial on an interval in terms of its degree squared and the norm of the polynomial itself, with the factor of degree squared being the optimal upper bound. Here we study what this factor should be on average, for random polynomials with independent N(0,1) coefficients. In the case of the interval [−1,1] and Jacobi weights defining an L2 space, we show that this average factor is order degree to the 3∕2, as compared to the degree squared worst case upper bound.
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