Self-interacting processes, supersymmetry, and Bayesian statistics
September 23 to September 27, 2019
American Institute of Mathematics,
San Jose, California
and Pierre Tarres
This workshop will be devoted to self-interacting
processes and their interaction with supersymmetry, Bayesian statistics and de
Non-Markovian random walks have emerged as a central topic in modern
probability, including models with long-memory effects produced by
self-interaction or the influence of a random media. Recent progress hints for
deep relations with supersymmetric field theory, Anderson localisation or some
theoretical aspects of Bayesian statistics. The meeting will gather experts from
different areas, aiming at a better understanding of these relations and at
developing new ideas to handle some of the most challenging models.
The main topics for the workshop are:
- Self-interacting processes (SIP). Several challenging self-interacting
processes, including once-reinforced process, nonlinear reinforced processes and
vertex reinforced process, do not have exchangeability property. Specific
techniques need to be developed for these models.
- Supersymmetry and Anderson localisation. The edge reinforced random walk
and vertex reinforced jump process have shown explicit relationships with the a
nonlinear supersymmetric sigma-model and a specific random Schroedinger operator.
Natural questions emerge from this correspondence such as: is this
correspondence a particular instance of a more general picture; what can be
learned from the techniques developed for Anderson localisation and what can be
proved for these SIP which is not accessible for Anderson localisation (e.g.
strong localisation in 2D)?
- de Finetti type theorems. One of the underlying forces at work is the
repeated reinvention of de Finetti type theorems, which appear in different
contexts as SIP, quantum information, Bose-Einstein condensation, etc., and have
applications in Bayesian statistics. The workshop will explore connections
between these complementary views.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.