Timeline for What is the best probabilistic estimate from below for a random polynomial on an arc?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Oct 14, 2017 at 5:27 | answer | added | TOM | timeline score: 1 | |
| Feb 20, 2013 at 14:26 | history | edited | fedja | CC BY-SA 3.0 |
posted an update
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| Dec 13, 2012 at 4:01 | comment | added | fedja | I'm not sure if it has really appeared in print yet but the result was obtained simultaneously by two pairs of people: Krishnapur and Zeitouni, and Kabluchko and Zaporozhets. Misha Sodin kindly told me the sketch of the proof. Divide by $1-x$. Then the sequence of the coefficients will become $\xi_1,\xi_1+\xi_2,\dots,\xi_1+\dots+\xi_n$, after which it stabilizes. Now just use Descartes' rule of signs and the fact (not sure how well known) that any $n$-step random walk on the line with i.i.d. steps cannot change sign more than $C\sqrt n$ times on average. | |
| Dec 12, 2012 at 17:38 | comment | added | Mark Meckes | Can you give a reference for the $C\sqrt{n}$ bound (or an indication of the proof if it's easy)? A little quick googling turns up lots of literature on the problem, but I didn't immediately find that. | |
| Dec 12, 2012 at 1:32 | history | asked | fedja | CC BY-SA 3.0 |