Timeline for A variation of the law of large numbers for random points in a square
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 10, 2020 at 16:07 | vote | accept | Nikita Kalinin | ||
| Jun 10, 2020 at 7:02 | answer | added | van vu | timeline score: 12 | |
| Jun 10, 2020 at 3:45 | answer | added | Yuval Peres | timeline score: 26 | |
| Jun 10, 2020 at 1:24 | answer | added | Vlad Vysotsky | timeline score: 3 | |
| Jun 9, 2020 at 23:02 | answer | added | Gustave Emprin | timeline score: 4 | |
| Jun 9, 2020 at 16:56 | answer | added | Guillaume Aubrun | timeline score: 8 | |
| Jun 9, 2020 at 16:21 | history | became hot network question | |||
| Jun 9, 2020 at 14:54 | comment | added | Vlad Vysotsky | @Nikita Kalinin It is a nice problem! But somehow I share Iosif Pinelis's scepticism that cn would not suffice. You do have a reasonably quick algorithm how to compute the cuts for a given realisation of points, do not you? | |
| Jun 9, 2020 at 14:17 | answer | added | Iosif Pinelis | timeline score: 6 | |
| Jun 9, 2020 at 14:03 | comment | added | Vlad Vysotsky | @Nikita Kalinin Of course, this is the main point (and difficulty)! Otherwise the claim will not work, as per the answer attempts below. It is unclear to me why your problem should in a sense correspond to some law of large numbers. | |
| Jun 9, 2020 at 13:53 | comment | added | Nikita Kalinin | @Vysotsky note also that we cut AFTER we marked points randomly, so there is more freedom. | |
| Jun 9, 2020 at 12:29 | answer | added | Dieter Kadelka | timeline score: 0 | |
| Jun 9, 2020 at 11:58 | comment | added | Nikita Kalinin | @Vysotsky not a heuristics, but a somewhat weaker statements can be observed experimentally and it would follow from the positive answer to my question. The statement is that the degree of a tropical curve through n^2 random points in a square is concentrated near n. | |
| Jun 9, 2020 at 11:42 | comment | added | Vlad Vysotsky | What's you heuristics for the suggestion that the probability goes to one? As a side comment, there are results describing the asymptotics of the side of the largest empty square with sides parallel to those of [0,1]^2. A version of rectangles instead of squares also exist, I think. The proof is, however, is not a LLN-type one. | |
| Jun 9, 2020 at 9:50 | answer | added | mike | timeline score: 2 | |
| Jun 9, 2020 at 8:35 | history | edited | Nikita Kalinin | CC BY-SA 4.0 |
deleted 2 characters in body
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| Jun 9, 2020 at 8:21 | history | asked | Nikita Kalinin | CC BY-SA 4.0 |