Density of critical points for a Gaussian random function

  title={Density of critical points for a Gaussian random function},
  author={Hendrik Vogel and W.Mohring},
Critical points of a scalar quantitiy are either extremal points or saddle points. The character of the critical points is determined by the sign distribution of the eigenvalues of the Hessian matrix. For a two-dimensional homogeneous and isotropic random function, topological arguments are sufficient to show that all possible sign combinations are equidistributed or with other words, the density of the saddle points and extrema agree. This argument breaks down in three dimensions. All ratios… CONTINUE READING