  Finding the mean of the total number of stationary points for N-dimensional
random Gaussian landscapes can be reduced to averaging the absolute value of
characteristic polynomial of the corresponding Hessian. First such a reduction
is illustrated for a class of models describing energy landscapes of elastic
manifolds in random environment, and a general method of attacking the problem
analytically is suggested. Then the exact solution to the problem [Phys. Rev.
Lett. v.92 (2004) 240601] for a class of landscapes corresponding to the
simplest, yet nontrivial "toy model" with N degrees of freedom is described.
Asymptotic analysis reveals a phase transition to a glass-like state of the
matter.
