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- W3107373089 abstract "Finding the mean of the total number Ntot 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[1] for a class of landscapes corresponding to the simplest, yet nontrivial ”toy model” with N degrees of freedom is described. For N ≫ 1 our asymptotic analysis reveals a phase transition at some critical value μc of a control parameter μ from a phase with finite landscape complexity: Ntot ∼ e, Σ(μ 0 to the phase with vanishing complexity: Σ(μ > μc) = 0. This is interpreted as a transition to a glass-like state of the matter." @default.
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- W3107373089 date "2005-09-01" @default.
- W3107373089 modified "2023-09-26" @default.
- W3107373089 title "Counting Stationary Points of Random Landscapes as a Random Matrix Problem" @default.
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