Small eigenvalues of closed Riemann surfaces for large genus

In this article we study the asymptotic behavior of small eigenvalues Riemann surfaces for large genus. We show that any positive integer $k$, as genus $g$ goes to infinity, smallest $k$-th eigenvalue in thick part moduli space is uniformly comparable $\frac{1}{g^2}$ $g$. proof upper bound, constant $\epsilon>0$, will construct a closed surface $\epsilon$-thick such it admits pants decomposition whose boundary curves all have length equal $\epsilon$, and number separating systole