For every n≥3, non-trivial solutions on the simplex lattice Δ_N^{(n)} and on Z^n have at least c N^{⌈n/2⌉} (resp. c L^{⌈n/2⌉}/log L) sites where the value is not exponentially small.
Localization and unique continuation for the Anderson-Bernoulli model with long-range hopping on $\mathbb{Z}$
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this paper, we study Anderson localization near the spectral edge for the Anderson-Bernoulli model on $\mathbb{Z}$ with long-range hopping. When the hopping has a rational Laurent symbol, a quantitative version of the unique continuation principle can be proved, and localization occurs. For the unique continuation in the general case, we give some counterexamples and prove a weaker result for hopping that decays faster than exponential rate. To the best of our knowledge, this is the first localization result for the long-range Anderson model with pure Bernoulli potentials.
fields
math.AP 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Quantitative Unique Continuation on Simplex and $\mathbb{Z}^n$
For every n≥3, non-trivial solutions on the simplex lattice Δ_N^{(n)} and on Z^n have at least c N^{⌈n/2⌉} (resp. c L^{⌈n/2⌉}/log L) sites where the value is not exponentially small.