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.

Brett Kolesnik received a PhD in Mathematics, advised by Prof Omer Angel in the UBC Probability Group. He then held postdoctoral fellowships at the University of California, Berkeley and San Diego, and the University of Oxford. He is currently an Assistant Professor at the University of Warwick.