Timeline for Least positive value of a random polynomial
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 19, 2021 at 0:39 | comment | added | Iosif Pinelis | @Dr.Pi : I think that your questions (in the current form) can be restated simply as follows. Question 1: What is $P(\inf f\ge0)$? Question 2: What are rough bounds on $P(\inf f>z)$ as $z\to\infty$? | |
| Sep 18, 2021 at 19:25 | history | edited | Dr. Pi | CC BY-SA 4.0 |
added 653 characters in body; edited tags
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| Sep 18, 2021 at 18:58 | comment | added | Dr. Pi | Indeed, I totally forgot that the polynomials may take only negative values. I will edit the question. | |
| Sep 18, 2021 at 16:17 | comment | added | Yuval Peres | My guess is that the OP did not intend to include the event $\{\sup f \le 0\}$. Let's wait for clarification. | |
| Sep 17, 2021 at 18:18 | comment | added | Iosif Pinelis | @FedorPetrov : I think the question is to estimate, for large $z>0$, the probability of the union of the following two events: (i) $\{\sup f\le0\}$ (on which we have $m_f=\infty$) and (ii) $\{\inf f>z\}$. | |
| Sep 17, 2021 at 17:56 | comment | added | Fedor Petrov | Why do you add $f(x) >0$ condition in the definition of $m_f$? | |
| Sep 17, 2021 at 15:19 | history | asked | Dr. Pi | CC BY-SA 4.0 |