Self-interacting processes, supersymmetry, and Bayesian statistics

Original Announcement

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

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop: