##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability & Statistics Seminar

## Hoi Nguyen

#### Ohio State University

## On real roots of random Bernoulli polynomials

##### Abstract:

By using a simple method, we show that a random $\pm 1$ 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 $(2/\pi)(\log n) + C + o(1)$ for some absolute constant $C$. The method extends to more general coefficient distributions. (Based on joint work with O. Nguyen and V. Vu)

Host: Jason Schweinsberg

### May 29, 2014

### 10:00 AM

### AP&M 6402

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