Dependence of two random quantities is most commonly measured through the correlation coefficient. A widespread misconception about the correlation coefficient is that its minimum value is always equal to the lower bound, that is -1. Minimum and maximum actually depend on distributions in question, and the explicit answers are not known even for some very well studied cases. The situation gets much more complicated as the number of variables increases and very little is known about correlation ranges in higher dimensions. Answers to these questions are perhaps most valuable for data analysis, as it is critical knowing theoretically possible ranges in order to put sample correlation into right perspective.

This talk with approach the above topic focusing on computational problems of type: How to simulate exactly a random vector (X1,...,Xn) with given marginals and a correlation matrix, only?
I will discuss our recent results (theorems and algorithms) in this direction and also present a connection with 0/1 Polytopes.