Abstract:
In the ballistic annihilation model, particles are emitted from a Poisson point process on the line, move at constant speed (chosen i.i.d. at initial time) and mutually annihilate when they collide. This model was introduced in the 1990's in physics, however its asymptotic behavior remains very poorly understood as soon as the speeds may take at least three values. We will focus on this minimal case when speeds may equal -1, 0 or 1, with symmetric probabilities, and show in particular that a phase transition takes place when the speed 0 has probability 1/4. This is based on joint work with J. Haslegrave and V. Sidoravicius.
Biography:
Laurent Tournier graduated at the École Normale Supérieure in Paris before receiving his Ph.D. 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 Université Paris 13 as an Assistant Professor. His main research interests focus on random walks in random environment, reinforced random walks, particle systems and statistical mechanics.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai