Mini-Workshop: Geometry of Random Fields and Random Walk Clusters: New Horizons

Abstract

Critical phenomena represent a central theme in probability. Research has been going on for many decades and remains very active to date. Recently, models involving natural probabilistic objects such as random walks, loop soups, random interlacements and the Gaussian free field have witnessed exciting developments, both in two- and higher-dimensional setups. The purpose of the workshop was to provide an overview of the state of the art in this rapidly evolving research area. The workshop enabled participants to communicate about the most recent advances in the field, and to discuss propitious avenues for future research.