Timeline for Distinct eigenvalues of random matrix over finite field
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 30 at 9:00 | vote | accept | darko | ||
| Oct 29 at 16:01 | comment | added | Will Sawin | @darko 1. I'm just using $A$ as a formal variable instead of a random variable. Since this is confusing, I have replaced the formal variable with $T$. 2. Added the argument. No, $M$ is not a fixed vector subspace but a fixed module, with a fixed surjective homomorphism, thus rendering it a fixed quotient space. | |
| Oct 29 at 15:59 | history | edited | Will Sawin | CC BY-SA 4.0 |
added 1187 characters in body
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| Oct 29 at 15:05 | comment | added | darko | Great, thank you! I am a bit confused about how exactly you are using the randomness of $A$ in your argument (in the paragraph about the expectation of the number of quotients). I would be grateful if you could clarify this. 1. Are you taking expectation in $A$? The end result $1/|\mathrm{Aut}_{\mathbf{F}_p[A]}(M)|$ depends on $A$ and in particular on $M$ as an $A$-module. 2. Why is a surjection of $\mathbf{F}_p$-modules a surjection of $\mathbf{F}_p[A]$-modules with probability $1/|\mathrm{Hom}_{\mathbf{F}_p}(\mathbf{F}_p^n, M)|$? Is $M$ supposed to be a fixed vector subspace here? | |
| Oct 27 at 9:54 | vote | accept | darko | ||
| Oct 29 at 14:42 | |||||
| Oct 25 at 15:31 | history | answered | Will Sawin | CC BY-SA 4.0 |