Connecting the q-multiplicative convolution and the finite difference convolution

Multiplicative complexity, convolution, and the DFT

Well, someone can decide by themselves what they want to do and need to do but sometimes, that kind of person will need some multiplicative complexity convolution and the dft references. People with open minded will always try to seek for the new things and information from many sources. On the contrary, people with closed mind will always think that they can do it by their principals. So, what...

Convolution and Homogeneous Spaces

Quadrature for the Finite Free Convolution

These notes are not necessarily an accurate representation of what happened in class. The notes written before class say what I think I should say. I sometimes edit the notes after class to make them way what I wish I had said. There may be small mistakes, so I recommend that you check any mathematically precise statement before using it in your own work. These notes were last revised on Decemb...

Probability MULTIPLICATIVE FREE CONVOLUTION AND INFORMATION - PLUS - NOISE TYPE MATRICES

Free probability and random matrix theory has shown to be a fruitful combination in many fields of research, such as digital communications, nuclear physics and mathematical finance. The link between free probability and eigenvalue distributions of random matrices will be strengthened further in this paper. It will be shown how the concept of multiplicative free convolution can be used to expre...

Spectral density of generalized Wishart matrices and free multiplicative convolution.

We investigate the level density for several ensembles of positive random matrices of a Wishart-like structure, W=XX(†), where X stands for a non-Hermitian random matrix. In particular, making use of the Cauchy transform, we study the free multiplicative powers of the Marchenko-Pastur (MP) distribution, MP(⊠s), which for an integer s yield Fuss-Catalan distributions corresponding to a product o...