Shihe Liu

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3 papers · 1 filter

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.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.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

Anderson Localization for the hierarchical Anderson-Bernoulli model on Zd

Anderson localized states for the nonlinear Maryland model on Zd

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

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

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