  Observations of high-redshift quasars hosting billion solar mass black holes
at $z\gtrsim6$ challenge our understanding of early supermassive black hole
(SMBH) growth. In this work, we conduct a near-infrared spectroscopic study of
$19$ quasars at $6.2\lesssim z\lesssim 7.5$, using the Folded-port InfraRed
Echellette (FIRE) instrument on the $6.5$-meter Magellan/Baade Telescope. We
estimate the single-epoch masses of the quasars' SMBHs by means of the MgII
emission line and find black hole masses of $M_{\text{BH}}
\approx(0.2-4.8)\,\times\,10^9\,M_\odot$. Furthermore, we measure the sizes of
the quasars' proximity zones, which are regions of enhanced transmitted flux
bluewards of the Ly$\alpha\,$ emission line, ionized by the quasars' radiation
itself. While it has been shown that the proximity zone sizes correlate with
the quasars' lifetimes due to the finite response time of the intergalactic
medium to the quasars' radiation, we do not find any correlation between the
proximity zone sizes and the black hole mass, which suggests that quasar
activity and the concomitant black hole growth are intermittent and episodic.
