Two Problems Based on Uniform Non Crossing Matchings on the Integers

Uniform rooted trees with n edges are classically mapped to random walk excursions of length 2n and to uniform non crossing matchings on the integer interval 1..2n. The extension to the full-line provides a combinatorially rich object; we will present two problems based on it. In the first one, stemming from random map theory, we will investigate the structure of the graph obtained by superposing two independent such infinite matchings. In the other one, we will interpret this matching in terms of annihilating particles and discuss another puzzling question.

This is based on joint works with Nicolas Curien, Gady Kozma and Vladas Sidoravicius.

 

Laurent Tournier graduated at the École Normale Supérieure in Paris before receiving his PhD in mathematics at the University of Lyon, France, in 2010. After a postdoc position in Rio de Janeiro, Brazil, he moved in 2011 to the University Paris Nord 13 as an assistant professor. His main research interests focus on random walks in random environment, reinforced random walks, particle systems and statistical mechanics.