Graduate Program in Mathematics.Yılmaz Atilla.Yenisey, Mehmet.2023-03-162023-03-162015.MATH 2015 Y46https://digitalarchive.library.bogazici.edu.tr/handle/123456789/15279Large deviations is a branch of probability theory with far-reaching applications in other elds 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 Erd}os-Kac theorem on the number of distinct prime factors of a uniformly chosen random natural number less than or equal to n.30 cm.Markov processes.vii, 66 leaves ;