David Dudaš

One spin per correlation volume: a conditional Simon inequality and the cost of reading a ferromagnet

How many spins of a ferromagnet must one observe to learn its magnetization? For the ferromagnetic Ising model in zero field on a finite graph we prove that, for every set U of observed sites and all sites x, y, E[ E[σ_x | σ_U] E[σ_y | σ_U] ] ≤ Σ_{u∈U} ⟨σ_x σ_u⟩⟨σ_u σ_y⟩. This extends Simon's correlation inequality fro...