A law of large numbers concerning the distribution of critical points of random Fourier series

Qiangang "Brandon'' Fu, Liviu I. Nicolaescu

On the flat torus ${\mathbb{T}}^m={\mathbb{R}}^m/{\mathbb{Z}}^m$ with angular coordinates $\vec{\hat{I}}¸$ we consider the random function $F_R=\mathfrak{a}(R^{-1}\sqrt{\hat{I}}”)W$, wher…