Zhi-Jun Cai | Searcharxiv

arXiv2026

Refined Berry-Esseen bounds under local dependence

In this paper, we establish Berry--Esseen bounds for both self-normalized and non-self-normalized sums of locally dependent random variables. The proofs are based on Stein's method together with a concentration inequality approach. We develop a new class of concentration inequalities that extend classical results and achieve optimal convergence rates under more general dependence structures. As applications, we apply our main results to derive sharper Berry--Esseen bounds for graph dependency, distributed $U$-statistics, constrained $U$-statistics, and decorated injective homomorphism sums.

math.PR↗

arXiv2016

Topologically trivial and nontrivial edge bands in graphene induced by irradiation

We proposed a minimal model to describe the Floquet band structure of two-dimensional materials with light-induced resonant inter-band transition. We applied it to graphene to study the band features caused by the light irradiation. Linearly polarized light induces pseudo gaps (gaps are functions of wavevector), and circularly polarized light causes real gaps on the quasi-energy spectrum. If the polarization of light is linear and along the longitudinal direction of zigzag ribbons, flat edge bands appear in the pseudo gaps, and if is in the lateral direction of armchair ribbons, curved edge bands can be found. For the circularly polarized cases, edge bands arise and intersect in the gaps of both types of ribbons. The edge bands induced by the circularly polarized light are helical and those by linearly polarized light are topologically trivial ones. The Chern number of the Floquet band, which reflects the number of pairs of helical edge bands in graphene ribbons, can be reduced into the winding number at resonance.

cond-mat.mes-hall↗