New Directions in Random Spatial Processes

The goal of this workshop is to highlight emerging new topics in spatial probability, and related areas where probabilistic ideas play an important role. The emphasis is on types of questions and approaches that are not largely based on existing techniques. We have invited researchers with a variety of backgrounds, to help cross-fertilization between areas. Some topics that the organizers have in mind are below, although speakers have the freedom to choose what they find suitable.

Combinatorial optimization problems with a stochastic component are a source of challenging open questions. Examples are the traveling salesman problem on a random set of points, other optimal path problems on random data, and allocation problems. Heuristics from statistical physics often suggest conjectures, open to investigation. Interacting spatial processes has been an active area since the 1970s, with interesting connections to other fields of mathematics such as random permutations, and PDEs. Such processes with non-local interactions have not been studied extensively. Interesting examples of deterministic processes have been found, where randomness plays a role in the analysis, such as crystal growth or sandpiles. These types of connections between deterministic and random are likely to be the source of intriguing questions in the future.