Timeline for A question about the square root error of one dimensional random walks
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 17, 2023 at 10:56 | comment | added | Carlo Beenakker | it's elementary, really: if $x_N$ is the position of the random walker after $N$ steps, then $d_N=|x_N-x_0|$ and $s_N=x_N-x_0$. | |
| Jan 17, 2023 at 10:06 | comment | added | EGME | Is this average distance relative to the displacement average which is zero? Do you know a reference where all these concepts are defined? My understanding comes from reading papers which are not specifically about this. Thanks in advance | |
| Jan 17, 2023 at 9:59 | comment | added | Carlo Beenakker | it is common to call $\langle d_N\rangle$ the "average distance" after $N$ steps; "square root error" refers to the displacement $s_N$, which has zero average and variance ${\rm var}\,(s_N)=\mathbb{E}(s_N^2)=(1-r)N$, so rms value $\sqrt{(1-r)N}$. | |
| Jan 17, 2023 at 9:31 | comment | added | EGME | Thank you. Do you happen to know where the term "square root error" comes from? I am looking for a reference if there is one. Or, alternatively, what is the common term for $\langle d_N \rangle$? I thank you in advance. | |
| Jan 16, 2023 at 12:27 | vote | accept | EGME | ||
| Jan 16, 2023 at 9:56 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
added 107 characters in body
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| Jan 16, 2023 at 9:50 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |