Timeline for Expected determinant of a random NxN matrix
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Jun 13, 2022 at 15:56 | comment | added | Terry Tao | By multiplying rows and columns by signs, one can normalise the first row and column to be all 1s. If one then subtracts the first row from all the others to make the first column (1,0,...,0), the bottom right n-1 x n-1 minor is now a random matrix of 0s and -2s, whose determinant is $(-2)^{n-1}$ times that of a random 0-1 matrix. The various sign factors one incurs in this process can then be removed by interchanging some rows (assuming $n>2$). | |
| Jun 12, 2022 at 23:36 | comment | added | Machinato | How exactly was the Gaussian elimination carried over? I mean how can one get from (-1,+1) ran. matrix to another (0,1) ran. matrix | |
| Jul 2, 2015 at 15:46 | comment | added | Terry Tao | Update: the central limit theorem for the log-determinant was worked out carefully by Nguyen and Vu, arxiv.org/abs/1112.0752 | |
| Jun 9, 2010 at 21:03 | history | answered | Terry Tao | CC BY-SA 2.5 |