Slide 13 of 19
Notes:
This picture shows how objects (assets of the S&P500 index) freeze into clusters as the parameter b increases. For each b, we define pis(b) as the probability to find object i in cluster s, i.e. si=s. The entropy of this distribution gives a measure of the (logarithm of the) number of clusters “visited” by object i. This is plotted, for each object, versus the strength Sspis(b) /(1+gs) of the independent noise ei(t) acting on that object. We see clearly that as b increases objects tend to localize into clusters: The number of clusters they visit is smaller.
