Another common used definition is that

\sum_{i,j} |X_i||X_j| \le \epsilon |V|^{2}.

The above two definitions are more or less equivalent, if all the parts almost have the same size.

However, at a talk of Jacob Fox, (2017, Berkeley), he used the following:

irreg(P) \le \epsilon |V|^{2}.

I did not see why this definition is equivalent to the above definitions. Or are they equivalent at all ?

(Maybe the correct definition should be irreg(P) \le \epsilon^{2} |V|^{2}? )

Thanks.

]]>I am delighted to have found your blog. I would like to know whether you’d recommend some particular reading for someone interested in learning about graph limits (apart from the original articles by Lovász and collaborators). My first encounter with the formalism was through Chatterjee and Diaconis (Estimating and Understanding Exponential Random Graphs), and would like to read more about it. Thanks!

]]>Excellent post on regularity lemma and triangle removal lemma. ]]>