Three-speed ballistic annihilation

02.05.2022 15:15 – 17:15

Ballistic annihilation is a 1-dimensional model where particles initially positioned according to a Poisson point process move at i.i.d. constant speeds; when two particles meet they are both destroyed. The simplest version admitting a non-trivial phase transition is the symmetric three-speed case, where speeds are -1,0,+1 with -1 and +1 being equally likely. This model appears in the physics literature in the 1990s, where it was predicted, supported by intricate calculations, that a phase transition occurs when the probability of speed 0 reaches 1/4, with particles being destroyed with probability 1 below that point, but surviving with positive probability above it. More recently, it came to the attention of mathematicians, but despite several upper bounds on the critical probability, a non-trivial rigorous lower bound was elusive. I will talk about a combinatorial proof of the precise phase transition, which also yields much more information including the asymptotic decay of particles. If time permits, I will also discuss recent extensions by other authors. This is joint work with Laurent Tournier and the late Vladas Sidoravicius.

Lieu

Salle 1-15, Séminaire "Mathématique physique"

entrée libre