There is a paper entitled: "Random Vandermonde Matrices-Part I: Fundamental results" that I wish to understand some math handling steps. The manuscript can be downloaded from https://documents.epfl.ch/groups/i/ip/ipg/www/2009-2010/Random_Matrices_and_Communication_Systems/ryan.pdf
The problem is that the content is based on free probability theory and I am struggling to understand the manuscript. I am interested in calculating the moments of a Vandermonde Matrix with random variable arguments. The equation (11) is the final result. The author gives results for up to 5 moments, but I would like to calculate more myself.
I think that I miss important concepts from the math theory there. I always get stuck on the math syntax and can't understand what is the actual function of the symbols (Like the concept of the partition sets). So, can someone point out some references ou explain some concepts for me?
Best Regards!