Timeline for Poisson spacings?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| May 8, 2021 at 20:08 | comment | added | Dr. Pi | thank you for the comment ofer. I edited-please let me know if that is ok and I am happy to edit again. I am very sorry for the confusion! Actually I am a bit confused about the averaged spacing: shouldnt it be 1 instead of $1/\sqrt n $? Sorry if this is wrong! | |
| May 8, 2021 at 20:07 | history | edited | Dr. Pi | CC BY-SA 4.0 |
added 118 characters in body
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| May 8, 2021 at 17:54 | comment | added | ofer zeitouni | @Dr. Pi If you want an answer, probably you should edit the question to reflect what you mean. I believe the formulation you just wrote makes no sense either, since the average spacing will be of order $1/\sqrt{n}$ then. The man of course changes nothing. | |
| May 8, 2021 at 16:52 | comment | added | Dr. Pi | @oferzeitouni Indeed, this is a very good point! I think I was probably having in mind to ask for $X^{(I+1)}-X^{(i)} > z $ instead. Where $X^{(i)} $ is the I-th smallest value. | |
| May 8, 2021 at 16:46 | comment | added | Nicolas Rivera | I am not sure about the limiting constant, but it seems that a first and second moment computation will get you the answer | |
| May 8, 2021 at 16:41 | comment | added | ofer zeitouni | Something is off in your formulation. Note that $X_n$ normal of mean $n$ and variance $n$ follows your assumptions. Now for $i$ even, the sequence $X_{i+1}-X_i$ is i.i.d., and $P(X_{i+1}-X_i>z)\to 1/2$ for any $z$. So by the LLN, the expression you wrote is at least $1/4$, whp, regardless of $z$. In fact, it converges to $1/2$. | |
| May 8, 2021 at 16:13 | history | asked | Dr. Pi | CC BY-SA 4.0 |