*[Corrected, thanks – T.]*

I have spent a couple of months trying to understand it but it seems impregnable but at the same time very important and deep.

Regards.

]]>For the sake of clompleteness let me mention that I wrote a paper about the spectral proof of the stronng regularity lemma which clarifies the same issues that you discuss (see below). It may also contain some new interesting aspect. (For example connection to graph limits and group theory)

Limits of kernel operators and the spectral regularity lemma

http://arxiv.org/abs/1003.5588

European J. of Comb, Volume 32, Issue 7, October 2011, p. 1156-1167

*[Thanks, I’e added a link to this in the main post. Good to see that we now have spectral proofs of the weak, strong, and standard regularity lemmas in the literature – T.]*

Even with my cynics hat on, I’m more inclined towards the weaker interpretation: referees have no *strong* incentive to actually understand a paper rather than just see if anything it says looks “obviously wrong”.

*[Corrected, thanks – T.]*

PS: Minor comment. One tag is misspelled as “eigenvales”.

*[Corrected, thanks -T.]*

So if I understood correct, there should still be a way to obtain Chung’s version in a simple algorithmic way as in the graph case suggested by Frieze and Kannan.

More precisely, there should be an analog of Lemma 2 in http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.721 for the higher order case.

That is, something along these lines must hold:

/// Let be a dimensional Tensor , with and . If is a small positive real number then,

(a) if there exists such that and then

(b) if then there exists such that and where , is a constant. Such might be constructed in polynomial time. ///

Is this a correct way of thinking about it?

]]>