Combinatorial applications of the Lévy–Khintchine formula
The Lévy–Khintchine formula relates an infinitely divisible probability measure to its Lévy measure, which controls the jumps of the associated Lévy process. If the Lévy measure is well behaved then the two measures are asymptotically equivalent (the one big jump principle). Using this framework, we will describe a solution to a 1968 conjecture of Leo Moser from the theory of graph tournaments. Connections with random walks, additive number theory, combinatorial geometry, and other applications will be discussed.