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On real roots of random Bernoulli polynomials

Mathematical Physics & Probability

Speaker: Hoi Nguyen, Ohio State University
Location: 2112 MSB
Start time: Wed, May 14 2014, 4:10PM

By using a simple method, we show that a random ±1 polynomial of degree n does not have double roots with probability tending to one (as n tends to infinity). As a consequence, we deduce that the expected number of real roots is (2/Ï)logn+C+o(1) for some absolute constant C. The method extends to more general coefficient distributions. (Based on joint work with O. Nguyen and V. Vu)