Timeline for A variation of the law of large numbers for random points in a square
Current License: CC BY-SA 4.0
7 events
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| Jun 20, 2020 at 19:17 | comment | added | Sandeep Silwal | A similar reasoning with the bound of $n^{4/3}$ also appears in the paper 'On Separating Points by Lines' by Har-Peled and Jones | |
| Jun 17, 2020 at 13:56 | comment | added | John Jiang | Very nice proof. I initially read the question wrong, and thought the grid was assumed uniform. But rather it can be actively chosen. A couple of points that I had to struggle with: the first estimate can be seen by realizing the binomial factor is 1 + o(1). For the constant 5, note removing a point can promote at most 4 grids to being good (2 on the same row and 2 on the same column), and adding a point can promote at most 1 grid, namely the grid where the point lands. Lastly for part b, two points are not on the same x or y cord with probably 1. How likely is it to get sharp estimate for c? | |
| Jun 10, 2020 at 16:07 | vote | accept | Nikita Kalinin | ||
| Jun 10, 2020 at 14:05 | history | edited | Yuval Peres | CC BY-SA 4.0 |
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| Jun 10, 2020 at 11:19 | history | edited | Yuval Peres | CC BY-SA 4.0 |
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| Jun 10, 2020 at 9:07 | comment | added | user21820 | Do you think the constant $k$ for which $p_n(k·n^{4/3}) → r ∈ (0,1)$ as $n→∞$ is rational or irrational? And what do you think it is? | |
| Jun 10, 2020 at 3:45 | history | answered | Yuval Peres | CC BY-SA 4.0 |