Timeline for Perturbation of Neumann Laplacian
Current License: CC BY-SA 4.0
14 events
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| S Mar 7, 2022 at 6:04 | history | bounty ended | CommunityBot | ||
| S Mar 7, 2022 at 6:04 | history | notice removed | CommunityBot | ||
| S Feb 27, 2022 at 4:06 | history | bounty started | Guido Li | ||
| S Feb 27, 2022 at 4:06 | history | notice added | Guido Li | Authoritative reference needed | |
| Feb 23, 2022 at 5:24 | comment | added | user7868 | Can you set up a recurrence relation for the $v_i$, using $\lambda v_{i-2}=-\alpha v_{i-4}-v_{i-3}+2(1+\alpha)v_{i-2}-v_{i-1}-\alpha v_i$? You have two boundary conditions, and you can fix $v_2$ arbitrarily, so you should get some equation involving $\lambda$ and $\alpha$, and your constraints on $\lambda$ would give you constraints on $\alpha$. | |
| Feb 23, 2022 at 4:16 | history | edited | Guido Li | CC BY-SA 4.0 |
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| Feb 22, 2022 at 19:58 | history | edited | Guido Li | CC BY-SA 4.0 |
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| Feb 22, 2022 at 17:33 | history | edited | Guido Li | CC BY-SA 4.0 |
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| Feb 22, 2022 at 17:32 | comment | added | Guido Li | @username I do not claim that $v_1$ and $v_N$ are independent of $N$. I claim that there exists $\varepsilon>0$ independent of $N$ such that for all $\alpha \in (0,\varepsilon)$ both $v_1, v_N$ are non-zero! | |
| Feb 22, 2022 at 15:42 | comment | added | username | did I miss something or in the case $\alpha=0$ the lower bound for the normalised eigenvector is $1/\sqrt N$ for $v_1$ or $v_N$ and therefore is not independent of $N$, in the link you provide? | |
| Feb 22, 2022 at 15:05 | history | edited | Guido Li | CC BY-SA 4.0 |
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| Feb 22, 2022 at 8:01 | history | edited | Guido Li | CC BY-SA 4.0 |
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| Feb 22, 2022 at 7:55 | history | edited | Guido Li | CC BY-SA 4.0 |
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| Feb 22, 2022 at 7:45 | history | asked | Guido Li | CC BY-SA 4.0 |