Large N Matrix Models and Noncommutative Fisher Information

Abstract

We interpret the action for 0+1‐dimensional large N matrix models in the context of noncommutative probability theory. The actions of both 0‐dimensional and 0+1‐dimensional matrix models contain universal terms, free entropy and free Fisher information respectively. Their minimization properties are essential for the solution of matrix models. We also give a geometric interpretation of the action principle of 0+1‐dimensional matrix models.