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Paul Erdős, one of the greatest mathematicians of the twentieth century, was a champion of applications of probabilistic methods in many areas of mathematics, such as a graph theory, combinatorics and number theory. He also, almost fifty years ago, jointly with another great Hungarian mathematician Alfred Rényi, laid out foundation of the theory of random graphs: the theory which studies how large and complex systems evolve when randomness of the relations between their elements is incurred. In my talk I will sketch the long journey of this theory from the pioneering Erdős era to modern attempts to model properties of large real world networks which grow unpredictably, including the Internet, World Wide Web (WWW), peer-to-peer, social, neural and metabolic networks.
Applied Mathematics | Mathematics
Karoński, Michał, "Random Graphs: From Paul Erdős to the Internet" (2009). Dalrymple Lecture Series. 7.