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Questions related to the spectrum of graphs, defined using one of the possible variants of the discrete Laplace operator or Laplacian matrix. See https://en.wikipedia.org/wiki/Discrete_Laplace_operator

2 votes
1 answer
160 views

Do product distributions (or graph products) eventually cluster as more products are taken?

Say we have a joint distribution on a finite alphabet $\mathcal{X}\times \mathcal{Y}$. It could be a communication link where we want to send a random message $X$ over a channel, but it gets garbled i …
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Do product distributions (or graph products) eventually cluster as more products are taken?

This conjecture is false in general. Unfortunately the only way I can think to prove this is through information theory. Consider a binary source $X\sim B(0.5)$ sent through an independent binary sy …
Christian Chapman's user avatar