Self-organized criticality is a term used to describe many physical systems (such as earthquakes and avalanches) where energy builds up slowly and then is released suddenly. One key feature of self-organized criticality is that the size of the release of energy has a fat tail. That is the probability that the energy release is bigger than some value k is decreasing polynomially in k. So far there has been limited success in proving that models from statistical physics exhibit self-organized criticality. One of the most promising mathematical models for self-organized criticality is called activated random walk. In this talk we will consider many different starting configurations for activated random walk on a line or a cycle. We will show that all of these have a critical density and all of those critical densities are the same. This is joint work with Toby Johnson and Matthew Junge.
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