Tel Aviv University

Dear all,

This week at the Horowitz seminar on Probability, Ergodic Theory and
Dynamical Systems at Tel Aviv University we are happy to have Fedor
Nazarov from Kent State University.
NOTE THE SPECIAL END TIME! The talk will be longer than usual.

Speaker: Fedor Nazarov, Kent State University

Title: Littlewood-Offord-Turan estimate for the number of real zeroes
of a random polynomial with i.i.d. coefficients

Date: Monday, December 31
Time: from 14:30 to 16:00!
Place: Schreiber 309

Abstract:
We show that the average number of real zeroes of any random
polynomial of degree $n$ with independent identically distributed
coefficients does not exceed $C\log^4 n$ with some absolute $C>0$.
The proof follows closely the paper by Littlewood and Offord
published in 1942, where the case of $\pm 1$ coefficients was
considered. Our main deviation from their scheme is using the Turan
lemma from Turan's 1953 book in place of the pointwise
"anticoncentration" estimate used by Littlewood and Offord. The
result is on par with the original Littlewood-Offord bound $C\log^2 n$ but still short of the would be optimal estimate $C\log n$, which
is widely believed to hold and whose validity is known for all
sufficiently regular distributions. This is a joint work with Mikhail
Sodin.

Best regards,

Ron

Seminar webpage:

<http://www.math.tau.ac.il/~peledron/Horowitz_seminar/Horowitz_seminar.html>

---------------------------------------------------------
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il>
Announcement from: Ron Peled   <peledron@post.tau.ac.il>