Randomly Hopping Majorana Fermions in the Diluted Kitaev System α-Ru0.8Ir0.2Cl3

dc and ac magnetic susceptibility, magnetization, specific heat, and Raman scattering measurements are combined to probe low-lying spin excitations in alpha-Ru_{1-x}Ir_{x}Cl_{3} (x approximately 0.2), which realizes a disordered spin liquid. At intermediate energies (variant Planck's over 2piomega>3 meV), Raman spectroscopy evidences linearly omega-dependent Majorana-like excitations, obeying Fermi statistics. This points to robustness of a Kitaev paramagnetic state under spin vacancies. At low energies below 3 meV, we observe power-law dependences and quantum-critical-like scalings of the thermodynamic quantities, implying the presence of a weakly divergent low-energy density of states. This scaling phenomenology is interpreted in terms of the random hoppings of Majorana fermions. Our results demonstrate an emergent hierarchy of spin excitations in a diluted Kitaev honeycomb system subject to spin vacancies and bond randomness.