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.
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