Abstract:Motivated by current interest in understanding statistical properties of random landscapes in highdimensional spaces, we consider a model of the landscape in R N obtained by superimposing M > N plane waves of random wavevectors and amplitudes. For this landscape we show how to compute the "annealed complexity" controlling the asymptotic growth rate of the mean number of stationary points as N → ∞ at fixed ratio α = M/N > 1. The framework of this computation requires us to study spectral properties of N × N mat… Show more
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