  The study of first passage times for diffusing particles reaching target
states is foundational in various practical applications, including
diffusion-controlled reactions. In this work, we present a bi-scaling theory
for the probability density function of first passage times in confined compact
processes, applicable to both Euclidean and Fractal domains, diverse
geometries, and scenarios with or without external force fields, accommodating
Markovian and semi-Markovian random walks. In large systems, first passage time
statistics exhibit a bi-scaling behavior, challenging the use of a single time
scale. Our theory employs two distinct scaling functions: one for short times,
capturing initial dynamics in unbounded systems, and the other for long times
is sensitive to finite size effects. The combined framework provides a complete
expression for first passage time statistics across all time scales.
