Critical clusters of the Gaussian free field on Z^3, Z^4 and Z^5 have tail exponent delta=(d+2)/(d-2) and largest-cluster dimension (d+2)/2, confirming Werner's conjectures.
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Cluster volumes for the Gaussian free field on metric graphs
Critical clusters of the Gaussian free field on Z^3, Z^4 and Z^5 have tail exponent delta=(d+2)/(d-2) and largest-cluster dimension (d+2)/2, confirming Werner's conjectures.