Particle systems and selection principles
Matthieu Jonckheere, University of Buenos Aires, Argentina
(Joint work with P. Groisman)
Abstract:
Nothing lasts forever. However many phenomena can be well described by
a process which enters a quasi-stationary state before eventually
vanishing. On the other hand, using a judicious state representation,
many phenomena (e.g. in chemistry, ecology, genetics, population
dynamics, telecommunications networks, statistical physics,...) can be
appropriately described by Markov processes.
Since the pioneering work of Kolmogorov and Yaglom, a lot of work has
been dedicated to understand the quasi-stationary behavior of Markov
processes. More precisely, for X a continuous time Markov process on a
countable state space, with an absorbing state that we call 0, the
conditioned evolution is the distribution of the process conditioned on
non-absorption while a quasi-stationary distribution (QSD) is a
probability measure that is invariant for the conditioned evolution.
We study different particles systems (Branching particles, Branching
with selection, Fleming Viot systems) that "select" minimal QSD and
eventually allow to simulate QSD distributions. We also explain some
links with the existence of traveling waves for some specific PDEs.
Aalto Stochastics & Statistics Seminar
Mon 8 Sep 2014, 16:15
Lecture Hall M2, Otakaari 1, Espoo