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We study concentration inequalities for the number of real roots of theclassical Kac polynomials $$f_{n} (x) = \sum_{i=0}^n \xi_i x^i$$ where $\xi_i$are independent random variables with mean 0, variance 1, and uniformly bounded$(2+\ep_0)$-moments. We establish polynomial tail bounds, which are optimal,for the bulk of roots. For the whole real line, we establish sub-optimal tailbounds.

Concentration inequalities for the number of real zeros of Kac polynomials