[Todos] Lattice permutations and Poisson-Dirichlet distribution of cycle lengths

[Pablo Groisman]

El lunes 15 de agosto a las 14.30hs en la Sala de Seminarios del
Departamento de Matemática (FCEN-UBA), Stefan Grosskinsky (University
of Warwick) dará una charla titulada

Lattice permutations and Poisson-Dirichlet distribution of cycle lengths


RESUMEN: We study random spatial permutations on Z^3 where each jump x
-> \pi(x) is penalized by a factor exp(-T ||x-\pi(x)||^2). Previous
simulation results strongly suggest that the system exhibits a phase
transition, where macroscopic cycles are present iff T is below a
finite critical value. We observe that the lengths of such cycles are
distributed according to Poisson-Dirichlet. This can be explained
heuristically using a stochastic coagulation-fragmentation process for
long cycles, which is supported by numerical data. This is joint work
with Alexander Lovisolo and Daniel Ueltschi.

Estan todos cordialmente invitados.