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Central Limit Theorems for global and local empirical measures of diffusions on Erdős-Rényi graphs
We address the issue of the Central Limit Theorem for (both local and global) empirical measures of diffusions interacting on a possibly diluted Erdős-Rényi graph. Special attention is given to the influence of initial condition (not necessarily i.i.d.) on the nature of the limiting fluctuations. We prove in particular that …