Bencs Ferenc: A Young-háló lokális spektrálmértékei

In this talk we will examine the local spectral measure of the Young-lattice as a graph, that is a graph on the irreducible representation of all the symmetric groups. This graph has been thoroughly investigated and it was observed by Stanley, that the local spectral measure of the vertex corresponding to the empty partition is the normal distribution. Building on these techniques, we will show that from any vertex the local spectral measure is absolutely continuous with respect to the Lebesgue-measure, moreover, its density function has the form $p_\lambda(x)\frac{1}{\sqrt{2\pi}}e^{-x^2/2}$, where $p_\lambda(x)$ is a polynomial that depends on the character table of $S_{|\lambda|}$.