In this paper, percolation theory is employed to place tentative bounds on the probability p of interstellar travel and the emergence of a civilization (or panspermia) that colonizes the entire Galaxy. The ensuing ramifications with regard to the Fermi paradox are also explored. In particular, it is suggested that the correlation function of inhabited exoplanets can be used to observationally constrain p in the near future. It is shown, by using a mathematical evolution model known as the Yule process, that the probability distribution for civilizations with a given number of colonized worlds is likely to exhibit a power-law tail. Some of the dynamical aspects of this issue, including the question of timescales and generalizing percolation theory, were also studied. The limitations of these models, and other avenues for future inquiry, are also outlined.Complex life-Extraterrestrial life-Panspermia-Life detection-SETI. Astrobiology 16, xxx-xxx.