Timeline for Exponential decay of voltage potential difference
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 26, 2020 at 15:30 | vote | accept | neverevernever | ||
| May 26, 2020 at 15:30 | vote | accept | neverevernever | ||
| May 26, 2020 at 15:30 | |||||
| May 25, 2020 at 15:34 | comment | added | neverevernever | Your updated solution is very insightful. It basically says that $e_1-e_2$ is in the span of the first two columns of $L$. When the entries of $L$ is not exactly $e^{-|i-j|}$, it seems intuitive that $e_1-e_2$ should also roughly lie within the span of the first several columns. The importance of each column to form the vector $e_1-e_2$ by linear combination seems to decay somehow. | |
| May 25, 2020 at 10:53 | history | edited | Mateusz Kwaśnicki | CC BY-SA 4.0 |
added 486 characters in body
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| May 24, 2020 at 0:16 | comment | added | Mateusz Kwaśnicki | (2/2) Regarding perturbations: I no longer trust my intuition here, but my wild guess would be "no", I think. The above approach seems to heavily use the structure of $e^{-|i-j|}$. | |
| May 24, 2020 at 0:14 | comment | added | Mateusz Kwaśnicki | (1/2) A miracle — indeed, I am completely surprised by this result, and I still do not understand how this is possible. I did once look at the continuous counterpart mentioned in the end of my answer and I noticed some nice explicit expressions, but with a different boundary condition. I am kind of shocked that with this particular definition one can still get explicit expressions. | |
| May 23, 2020 at 23:21 | comment | added | neverevernever | This is such a miracle! When the entries are not $e^{-|i,j|}$ exactly, for example we only have $e^{-|i-j|}\leq A_{ij}\leq 2e^{-|i-j|}$. Then I think they will not be exactly 0, can we bound $a_{kl}$ using similar arguments? | |
| May 23, 2020 at 21:09 | history | answered | Mateusz Kwaśnicki | CC BY-SA 4.0 |