Timeline for The expected max inner product between a random vector and the sum of random vectors
Current License: CC BY-SA 4.0
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| Mar 9 at 0:25 | vote | accept | Vezen BU | ||
| Mar 8 at 8:20 | answer | added | Sal | timeline score: 3 | |
| Mar 6 at 8:42 | history | edited | Vezen BU | CC BY-SA 4.0 |
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| Mar 6 at 8:35 | comment | added | Sal | Hi, no problem! Yes something like that- however note: the $\sqrt{n}$ scaling should be independent of the dimension so long as the step distributions are 'nice enough', while the constant $C_k$ may depend on the step distributions. In your case your steps are uniformly drawn on the $(k-1)$-sphere, while in the linked post the steps are are unit steps on a lattice, so they may differ- in your case it should be possible to evaluate at least $C_2$ explicitly. I'll think about it | |
| Mar 6 at 8:08 | history | edited | Vezen BU | CC BY-SA 4.0 |
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| Mar 6 at 8:03 | history | edited | Vezen BU | CC BY-SA 4.0 |
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| Mar 6 at 7:51 | comment | added | Vezen BU | @Sal Thank you! Is it something like this? math.stackexchange.com/questions/103142 | |
| Mar 6 at 7:08 | comment | added | Sal | $\sum_j^n X_j$ is a random walk in $k$ dimensions. If I recall correctly, the average absolute value of the random walk is asymptotically $C_k \sqrt{n}$ for some constant $C_k$ | |
| Mar 6 at 5:32 | history | edited | Vezen BU | CC BY-SA 4.0 |
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| Mar 6 at 5:24 | history | edited | Vezen BU | CC BY-SA 4.0 |
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| Mar 6 at 5:19 | history | edited | Vezen BU | CC BY-SA 4.0 |
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| Mar 6 at 5:10 | history | edited | Vezen BU | CC BY-SA 4.0 |
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| Mar 6 at 5:05 | answer | added | Chris Sanders | timeline score: 1 | |
| Mar 6 at 4:51 | history | edited | Vezen BU | CC BY-SA 4.0 |
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| Mar 6 at 4:45 | history | edited | Vezen BU | CC BY-SA 4.0 |
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| Mar 6 at 4:37 | history | edited | Vezen BU | CC BY-SA 4.0 |
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| Mar 6 at 4:31 | history | edited | Vezen BU | CC BY-SA 4.0 |
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| Mar 6 at 4:11 | history | edited | Vezen BU | CC BY-SA 4.0 |
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| Mar 6 at 4:07 | history | asked | Vezen BU | CC BY-SA 4.0 |