New critical exponent inequalities for percolation and the random cluster model
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Abstract
We apply a variation on the methods of Duminil-Copin, Raoufi, and Tassion to
establish a new differential inequality applying to both Bernoulli percolation
and the Fortuin-Kasteleyn random cluster model. This differential inequality
has a similar form to that derived for Bernoulli percolation by Menshikov but
with the important difference that it describes the distribution of the volume
of a cluster rather than of its radius. We apply this differential inequality
to prove the following:
The critical exponent inequalities
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2690-1005