• Corpus ID: 236635278

Subcritical Connectivity and Some Exact Tail Exponents in High Dimensional Percolation

@inproceedings{Chatterjee2021SubcriticalCA,
  title={Subcritical Connectivity and Some Exact Tail Exponents in High Dimensional Percolation},
  author={Shirshendu Chatterjee and Jack Hanson and Philippe Sosoe},
  year={2021}
}
In high dimensional percolation at parameter p < pc, the one-arm probability πp(n) is known to decay exponentially on scale (pc − p)−1/2. We show the same statement for the ratio πp(n)/πpc(n), establishing a form of a hypothesis of scaling theory. As part of our study, we provide sharp estimates (with matching upper and lower bounds) for several quantities of interest at the critical probability pc. These include the tail behavior of volumes of, and chemical distances within, spanning clusters… 

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