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Forest fires and coagulation-deletion processes

Presented by: 
JB Martin University of Oxford
Date: 
Thursday 15th August 2013 - 14:30 to 15:15
Venue: 
INI Seminar Room 1
Abstract: 
Consider the following extension of the Erdos-Renyi random graph process; in a graph on $n$ vertices, each edge arrives at rate 1, but also each vertex is struck by lightning at rate $\lambda$, in which case all the edges in its connected component are removed. Such a "mean-field forest fire" model was introduced by Rath and Toth. For appropriate ranges of $\lambda$, the model exhibits self-organised criticality. We investigate scaling limits, involving a multiplicative coalescent with an added "deletion" mechanism. I'll mention a few other related models, including epidemic models and "frozen percolation" processes.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons