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Lee Deville : Synchrony vs. Asynchrony due to Large Deviations in Stochastic Neuronal Networks

We consider idealized stochastic models for a network of pulse-coupled oscillators where there is randomness both in input and in network architecture. We describe the various types of dynamics which arise in this system, analyze scalings which arise in the infinite-network limit, and study the various "finite-size" effects as perturbations of these limits. Most notably, the networks we consider can simultaneously support both synchronous and asynchronous modes of behavior and will switch stochastically between these modes due to "rare events". We also relate the analysis of certain scaling limits of this network to classical graph-theoretical results involving the size of components in the Erdos-Renyi random graph. This work is joint with Charles Peskin and Joel Spencer.

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