A lower bound shows balanced multi-species spin glasses have free energy at least that of a single-species model with variance-matched couplings, and this bound is sharp in several regimes.
Injective norm of random tensors with independent entries
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We obtain a non-asymptotic bound for the expected injective norm of a random tensor with independent entries. This bound is similar to the bound by Bandeira and van Handel (2016) for the expected spectral norm of a random matrix with independent entries.
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Balanced multi-species spin glasses
A lower bound shows balanced multi-species spin glasses have free energy at least that of a single-species model with variance-matched couplings, and this bound is sharp in several regimes.