for this workshop
Self-interacting processes, supersymmetry, and Bayesian statistics
American Institute of Mathematics, San Jose, California
Persi Diaconis, Margherita Disertori, Christophe Sabot, and Pierre Tarres
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.
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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