Shihe Liu

collaborators

6 papers

math.AP2026

Quantitative Unique Continuation on Simplex and $Z^{n}$

Shihe Liu, Yunfeng Shi, Zhifei Zhang

In this work, we establish the quantitative unique continuation on both $n$ -dimensional simplex lattice $Δ_{N}^{(n)}$ and $Z^{n}$ for arbitrary $n \geq 3$ .

math.SP2026

Localization and unique continuation for the Anderson-Bernoulli model with long-range hopping on $Z$

Shihe Liu, Yunfeng Shi, Zhifei Zhang

In this paper, we study Anderson localization near the spectral edge for the Anderson-Bernoulli model on $Z$ with long-range hopping. When the hopping has a rational Laure…

math.AP2026

Anderson Localization for the hierarchical Anderson-Bernoulli model on $Z^{d}$

Shihe Liu, Yunfeng Shi, Zhifei Zhang

In this paper, we prove Anderson localization for a hierarchical Anderson-Bernoulli model on lattice with arbitrary dimension, where the potential is characterized by a geometric h…

math-ph2025

On localization for the alloy-type Anderson-Bernoulli model with long-range hopping

Shihe Liu, Yunfeng Shi, Zhifei Zhang

In this paper, we prove the Anderson localization near the spectral edge for some alloy-type Anderson-Bernoulli model on $Z^{d}$ with exponential long-range hopping. This ex…

math-ph2025

Extended states for the Random SchrÃ¶dinger operator on $Z^{d}$ ( $d \geq 5$ ) with decaying Bernoulli potential

Shihe Liu, Yunfeng Shi, Zhifei Zhang

In this paper, we investigate the delocalization property of the discrete SchrÃ¶dinger operator $H_{I ¨} = - I^ + v_{n} I ¨ _{n} I^´_{n, n^{'}}$ , where $v_{n} = I^º∣ n ∣^{- I^\pm}$ and $Ï=\{Ï_n\}_{n\in\mathbb{Z…

math.AP2025

Anderson localized states for the nonlinear Maryland model on $Z^{d}$

Shihe Liu, Yunfeng Shi, Zhifei Zhang

In this paper, we investigate Anderson localization for a nonlinear perturbation of the Maryland model $H = ε I^ + cot I ¨ (I^¸ + j \cdot I^\pm) I^´_{j, j^{'}}$ on $Z^{d}$ . Specificall…

Quantitative Unique Continuation on Simplex and Zn

Localization and unique continuation for the Anderson-Bernoulli model with long-range hopping on Z

Anderson Localization for the hierarchical Anderson-Bernoulli model on Zd

On localization for the alloy-type Anderson-Bernoulli model with long-range hopping

Extended states for the Random SchrÃ¶dinger operator on Zd (d≥5) with decaying Bernoulli potential

Anderson localized states for the nonlinear Maryland model on Zd

Quantitative Unique Continuation on Simplex and $Z^{n}$

Localization and unique continuation for the Anderson-Bernoulli model with long-range hopping on $Z$

Anderson Localization for the hierarchical Anderson-Bernoulli model on $Z^{d}$

Extended states for the Random SchrÃ¶dinger operator on $Z^{d}$ ( $d \geq 5$ ) with decaying Bernoulli potential

Anderson localized states for the nonlinear Maryland model on $Z^{d}$