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The Sandpile Model – A Simple Model for Cascades

Wiolette Ruszel

Delft University of Technology

The abelian sandpile model (ASM) is a toy model for “self-organised criticality”, a concept used to describe systems which drive themselves into a critical state without tuning a parameter. The ASM was also used in different disciplines such as biology or economy to model cascading failures. Since its birth year 87 this model has been extensively studied and different variants considered. This model is very interesting because of its many connections to different models and questions, such as chip-firing games, conformal field theory, bi-Laplacian Gaussian Fields and uniform spanning trees. In this talk we will introduce the basic model and review some of the many connections.