In the first part of this article, we proved a local version of the circular law up to the finest scale $N^{-1/2+ e}$ for non-Hermitian random matrices at any point $z in C$ with $||z| - 1| > c $ for any $c>0$ independent of the size of the matrix. U
nder the main assumption that the first three moments of the matrix elements match those of a standard Gaussian random variable after proper rescaling, we extend this result to include the edge case $ |z|-1=oo(1)$. Without the vanishing third moment assumption, we prove that the circular law is valid near the spectral edge $ |z|-1=oo(1)$ up to scale $N^{-1/4+ e}$.
We show by systemically experimental investigation that gas-flow-induced voltage in monolayer graphene is more than twenty times of that in bulk graphite. Examination over samples with sheet resistances ranging from 307 to 1600 {Omega}/sq shows that
the induced voltage increase with the resistance and can be further improved by controlling the quality and doping level of graphene. The induced voltage is nearly independent of the substrate materials and can be well explained by the interplay of Bernoullis principle and the carrier density dependent Seebeck coefficient. The results demonstrate that graphene has great potential for flow sensors and energy conversion devices.
