The critical mean-field random cluster model

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In a pair of papers in 2012 and 2010, Addario-Berry, Broutin and Goldschmidt showed the existence of, and gave the distribution for, the metric-space scaling limit of the Erdos-Rényi model in its critical regime, "critical" here referring to the critical point in the model's phase transition (a property first shown by Erdos and Rényi themselves). It is also known that several other random graph models possess a similar phase transition, with an analogous critical regime, such as the random cluster model, or various models of random planar graph. This project will explore a selection of such random graph models, with a view to proving similar scaling limit properties to those known for the Erdos-Rényi model.