Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm trying to understand this article: but I'm unsure what $\alpha(N)$ means in this context? Is it the algebraic multiplicity, that's pretty much the only $\alpha$ I have ever seen, but how does this make sense here? Also what is $o(N)$

share|cite|improve this question
I believe it means that there exists a function of $N$ called $\alpha$ such that "$\alpha(N)$ is little-o of $g(N)$", where $g(N)=N$ and the little-o notation is explained here. – Stefan Hansen Jan 15 '13 at 15:07

As in the definition of clustering, we want $\rho$ to converge to $0$ when $N\to \infty$, it's better to write it as $\rho_N$. By definition, $\rho_N\in[0,1)$. I didn't red the rest of the paper, but it probably helps to measure how $\rho_N$ behaves with respect to $1/N$, and that's the role played by the $\alpha_N$. Maybe it will be better writing $\rho_N\color{red}:=\frac{\alpha(N)}N$ in order to see it's defined like that.

As in clustering $\rho_N\to 0$, we can write $\alpha(N)$ as a product of $N$ with a function of $N$ converging to $0$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.