  One of the major puzzles in condensed matter physics has been the observation
of a Mott-insulating state away from half-filling. The filling-controlled Mott
insulator-metal transition, induced via charge-carrier doping, has been
extensively researched, but its governing mechanisms have yet to be fully
understood. Several theoretical proposals aimed to elucidate the nature of the
transition have been put forth, a notable one being phase separation and an
associated percolation-induced transition. In the present work, we study the
prototypical doped Mott-insulating rare-earth titanate YTiO$_3$, in which the
insulating state survives up to a large hole concentration of 35%. Single
crystals of Y$_{1-x}$Ca$_x$TiO$_3$ with $0 \leq x \leq 0.5$, spanning the
insulator-metal transition, are grown and investigated. Using x-ray absorption
spectroscopy, a powerful technique capable of probing element-specific
electronic states, we find that the primary effect of hole doping is to induce
electronic phase separation into hole-rich and hole-poor regions. The data
reveal the formation of electronic states within the Mott-Hubbard gap, near the
Fermi level, which increase in spectral weight with increasing doping. From a
comparison with DFT+$U$ calculations, we infer that the hole-poor and hole-rich
components have charge densities that correspond to the Mott-insulating $x = 0$
and metallic $x \sim 0.5$ states, respectively, and that the new electronic
states arise from the metallic component. Our results indicate that the
hole-doping-induced insulator-metal transition in Y$_{1-x}$Ca$_x$TiO$_3$ is
indeed percolative in nature, and thus of inherent first-order character.
