Activated Random Walk focused workshop

Activated random walk (ARW), an interacting particle model, has recently become a focal point in the development of the mathematical foundations of self-organized criticality (SOC), a wide-ranging theory of complex phenomena supported by strong statistical evidence. The participants of this workshop will aim to apply new mathematical tools (some of which were developed by the attendees themselves) to advance the theory of ARW in the context of discrete probability.

Possible specific goals:

1) Give rigorous statements and proofs of SOC conjectures, including critical scaling behavior and hyperuniformity;

2) Prove new properties of the limiting distribution of sleeping particles in the driven-dissipative version of ARW;

3) Describe the mean-field behavior of ARW by constructing scaling limit processes or measures.

The workshop will also be an opportunity for direct collaboration among an international group of researchers whose previous works approached ARW from different contexts, including analysis, probability, and combinatorics.