Resolution of the inverse-IDS hypothesis for unfolded Poisson statistics

Resolve the inverse-IDS hypothesis for local unfolded Poisson statistics of random polymer and ordinary Anderson–Bernoulli models under local Hölder regularity assumptions on the integrated density of states and its inverse.

Background

The paper discusses prior work of Germinet and Klopp and of Hislop and Nakano on unfolded Poisson statistics for random polymer models and the ordinary Anderson–Bernoulli model. The latter framework assumes local Hölder bounds for the integrated density of states N and its inverse N{-1}, with exponents satisfying a product condition.

The inverse-IDS assumption controls the physical width of unfolded energy windows in those arguments. The paper identifies this assumption as unresolved and contrasts its own exact-IDS-drift method, which avoids requiring a quantitative inverse-IDS modulus.

References

More recently, Hislop and Nakano Assumption~3.2, Theorem~3.3, and Corollary~1.7 treat random polymer models and the ordinary Anderson--Bernoulli model under local H\

— Poisson statistics for one-dimensional Anderson--Bernoulli Schrödinger operators  (2610.21268 - Han, 15 Oct 2026) in Section 1, subsection “Related work,” paragraph “IDS unfolding itself is established methodology”