Decay of the Green's function of the fractional Anderson model and connection to long-range SAW - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2023

Decay of the Green's function of the fractional Anderson model and connection to long-range SAW

Résumé

We prove a connection between the Green's function of the fractional Anderson model and the two point function of a self-avoiding random walk with long range jumps, adapting a strategy proposed by Schenker in 2015. This connection allows us to exploit results from the theory of self-avoiding random walks to improve previous bounds known for the fractional Anderson model at strong disorder. In particular, we enlarge the range of the disorder parameter where spectral localization occurs. Moreover we prove that the decay of Green's function at strong disorder for any $0<\alpha <1$ is arbitrarily close to the decay of the massive resolvent of the corresponding fractional Laplacian, in agreement with the case of the standard Anderson model $\alpha =1$. We also derive upper and lower bounds for the resolvent of the discrete fractional Laplacian with arbitrary mass $m\geq 0,$ that are of independent interest.

Dates et versions

hal-04335206 , version 1 (11-12-2023)

Identifiants

Citer

Margherita Disertori, Roberto Maturana Escobar, Constanza Rojas-Molina. Decay of the Green's function of the fractional Anderson model and connection to long-range SAW. 2023. ⟨hal-04335206⟩
17 Consultations
0 Téléchargements

Altmetric

Partager

More