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Jun 8, 2017 at 8:09 history edited Robert Bryant CC BY-SA 3.0
Fixed a few typos and the definition of phi
Jun 8, 2017 at 8:00 comment added Robert Bryant @LFH: Yes, you are right that I got carried away, oversimplifying the definition of $\phi$. I'll fix that.
Jun 8, 2017 at 6:39 comment added LFH Your answer was extremely helpful and very clear. Thank you very much! In your answer, you probably meant $A'_{ij}=\alpha^{|i-j|}$ where $|i-j|$ is the shortest distance with the $i$ thought to be arranged in a circle, meaning $1\equiv N+1$, but that's just for consistency with my question. I completely agree with your proof.
Jun 7, 2017 at 3:45 vote accept LFH
Jun 6, 2017 at 12:40 history edited Robert Bryant CC BY-SA 3.0
Added the promised proof
Jun 6, 2017 at 10:29 history answered Robert Bryant CC BY-SA 3.0