Author Archives: michaelngelo

Two little remarks on sphere

Posted on 15/04/2014 by michaelngelo

1. “Take a sphere of radius in dimensions, large; then most points inside the sphere are in fact very close to the surface.” David Ruelle Let and . Let The fraction of the volume of to the volume of is … Continue reading →

Posted in Geometry, Miscellaneous, Probability | Tagged , , | Leave a comment

Matrix multiplication as a convolution

Posted on 23/02/2014 by michaelngelo

1. The product of two power series/polynomials is The coefficients given by is sometimes called the Cauchy product. This is a convolution. 2. Let be a finite group and be the group algebra with complex coefficients. Let be two elements … Continue reading →

Posted in Analysis, Fourier analysis, Linear Algebra | Tagged , | Leave a comment

From combinatorics to entropy

Posted on 08/11/2013 by michaelngelo

Let and . Then by Stirling’s formula. This is probably well-known to people who have studied statistical physics, but some of us including myself may not be very aware of this kind of relation. I wonder if this was the … Continue reading →

Posted in Analysis, Probability | Tagged | Leave a comment

A meta post, and two articles

Posted on 11/05/2013 by michaelngelo

1. Is there any way to support MathJax here? It can translate directly the latex code to display math. It is supported on blogspot, I find it more convenient. 2. I believe many of us come across some very good articles … Continue reading →

Posted in Dynamical system, Uncategorized | 2 Comments

Fourier coefficients as eigenvalues/spectrum

Posted on 10/05/2013 by michaelngelo

In this post I want to make a connection between Fourier coefficients and eigenvalues/spectrum. Let me put the claim up front: If , then is not invertible with respect to the convolution product. Please feel free to jump directly to … Continue reading →

Posted in Fourier analysis, Linear Algebra | Tagged , | Leave a comment