Tags » Random Matrices

Random non-commutative geometry

Lisa Glaser and I have started to investigate random non-commutative geometries in our latest paper
Monte Carlo simulations of random non-commutative geometries. The geometries are all specified by a Dirac operator that is a finite-dimensional matrix, so in this theory the partition function is a finite-dimensional integral. 405 more words

Fundamental Physics

Curso: Introducción a la teoría clásica de matrices aleatorias

Notas del curso de 5 horas: “Introducción a la teoría clásica de matrices aleatorias” en la Facultad de Ciencias Físico-Matemáticas de la Universidad Autónoma de Sinaloa en la ocasión del XXXIII aniversario de la facultad (13-16 octubre 2015). 23 more words

Random Matrices

What is Random Matrix Theory?

With any question regarding mathematics as vague as the one I’ve just posed, I can’t give you an answer without at least lying a bit. Instead, I’ll do what any first course on RMT does — Wigner’s semi-circle law. 1,445 more words


Two Delightful Major Simplifications

Arguably mathematics is getting harder, although some people claim that also in the old times parts of it were hard and known only to a few experts before major simplifications had changed  matters. 278 more words


Random matrices have simple spectrum

Van Vu and I have just uploaded to the arXiv our paper “Random matrices have simple spectrum“. Recall that an Hermitian matrix is said to have simple eigenvalues if all of its eigenvalues are distinct. 612 more words


Some notes on Bakry-Emery theory

One of the most fundamental partial differential equations in mathematics is the heat equation

where is a scalar function of both time and space, and is the Laplacian . 3,326 more words


Random subspaces of a tensor product (II)

In this short post, I would like to discuss a special case of the construction introduced in the first part of the series, that is compute the set , where is the antisymmetric subspace of the tensor product. 316 more words

Random Matrices