Large deviations principles for Markov chains and for strongly additive arithmetic functions

Large deviations is a branch of probability theory with far-reaching applications in other fields of science and can be described to the layperson as the study of "very rare" events. We provide a modest introduction to the subject with an emphasis on large deviations behavior of continuous-time Markov chains and we present a recent result on large deviations related to the Erdös-Kac theorem on the number of distinct prime factors of a uniformly chosen random natural number less than or equal to "n".