What the paper shows is that often it is assumed that words drawn from an IID distribution of letters can be treated as if the distribution of words is uniform (given a sufficiently large word size). However, this distribution while very flat is not quite uniform. They show how this can be exploited using the "Guesswork" framework to come up with a tighter bound on the time it would take to guess a chosen word. This bound is much better than the traditional bound used.
By it being very flat but not uniform, what do you mean? I'm not clear on this point.
I mean that the distribution is very close to uniform. A uniform distribution is drawn a flat line when you graph it. (Inconstrast a normal distribution is a bell curve.) So when I say it is very flat I mean that it there is very little variation in the the pdf.
By it being very flat but not uniform, what do you mean? I'm not clear on this point.