Decay of Multi-point Correlation Functions in Zd.

We prove multi-point correlation bounds in Zd for arbitrary d ≥ 1 with symmetrized distances, answering open questions proposed by Sims-Warzel (Commun Math Phys 347(3):903-931, 2016) and Aza-Bru-Siqueira Pedra (Commun Math Phys 360(2):715-726, 2018). As applications, we prove multi-point correlation bounds for the Ising model on Zd , and multi-point dynamical localization in expectation for uniformly localized disordered systems, which provides the first examples of this conjectured phenomenon by Bravyi-König (Commun Math Phys 316(3):641-692, 2012) .