# Mean Field Behavior during the Big Bang for Coalescing Random Walk

@inproceedings{Hermon2021MeanFB, title={Mean Field Behavior during the Big Bang for Coalescing Random Walk}, author={J. Hermon and Shuangping Li and Dong Yao and Lingfu Zhang}, year={2021} }

In this paper we consider the coalescing random walk model on general graphs G = (V,E). We set up a unified framework to study the leading order of decay rate of Pt, the expectation of the fraction of occupied sites at time t, particularly for the ‘Big Bang’ regime where t≪ tcoal := E[inf{s : There is only one particle at time s}]. Our results show that Pt satisfies certain ‘mean field behavior’, if the graphs satisfy certain ‘transience-like’ conditions. We apply this framework to two families… Expand

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