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Mar 6 at 9:43 comment added Chris Sanders @VezenBU I still have a lot more to learn about probability distributions. Great question overall!
Mar 6 at 8:09 comment added Vezen BU Please see my update with @Sal's help. There are existing results on random walks.
Mar 6 at 6:58 comment added Brian Tung MathJax comment: Norms are better typeset using \|; for example, $\mathbb{E} \| \sum X_j \|_2$ yields $\mathbb{E} \| \sum X_j \|_2$.
Mar 6 at 5:53 comment added Vezen BU And this only solves the problem asymptotically.
Mar 6 at 5:42 comment added Vezen BU Yes! But seemingly that is a nontrivial problem.
Mar 6 at 5:37 comment added Chris Sanders Ah sorry yes that was a mistake, but the point still remains that it is just a matter of $\mathbb{E}||\sum X_j||_2$ @VezenBU
Mar 6 at 5:32 history edited Chris Sanders CC BY-SA 4.0
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Mar 6 at 5:20 comment added Vezen BU Thanks! But the last line is not immediate to me, although that looks true as $k \to \infty$.
Mar 6 at 5:17 history edited Chris Sanders CC BY-SA 4.0
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Mar 6 at 5:08 history undeleted Chris Sanders
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Mar 6 at 5:05 history answered Chris Sanders CC BY-SA 4.0