1. Introduction In the previous post, we saw how to use the replica method to calculate the spectral norm of the spiked GOE matrix. Besides the spectral norm, another interesting quantity of random matrices is the spectral density: the limiting empirical distribution of eigenvalues. In this post, we show how to calculate the spectral density of random matrices using the replica method. Let us take the GOE matrix as an example. The prerequisite knowledge for... … read more »
1. Introduction In my first several posts, I will discuss about the replica method. The replica method is a non-rigorous but powerful approach that originated within the statistical physics literature. It has been widely applied in other fields, including coding theory and high dimensional statistics. I used this method several times in my research. It helped me quickly figure out the answer of numerous problems. Most physicists know the replica method better than me. Here... … read more »
Hello everyone, I am starting my research blog today.
In my first several posts, I will discuss about methods from statistical physics, with applications to random matrix theory. Hope you will have fun!
… read more »