Drewitz, Alexander; Prévost, Alexis; Rodriguez, Pierre-François. Critical exponents for a percolation model on transient graphs. (English) Zbl 07662556 Invent. Math. 232, No. 1, 229-299 (2023).

Abstract

The authors study the bond percolation model obtained by considering the clusters of a weighted graph G (transient for the random walk on G) induced by the excursion sets of the Gaussian free field ϕ on the cable system G~ associated to G. They give two theorems describing the near-critical regime of the phase transition for the corresponding percolation model and derive various associated critical exponents, all of them functions of two parameters, ν and α, describing resp. the decay of correlations and the volume growth of G. The proofs make use of continuity and strong Markov properties and of potential theory.