Carptopus

Effective eventual monotonicity on the (2,2,m) tensor slice

Let a(n_1,...,n_p) denote the expected number of real critical rank-one approximations to a standard Gaussian tensor, in the normalization of Draisma and Horobeţ. We prove a(2,2,m) < a(2,2,m-1) for every integer m >= 3*10^103+3. The proof converts the Kac--Rice integral into an a...