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.

valeria ricci (2023). 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)..

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).

valeria ricci
2023-01-01

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.
2023
valeria ricci (2023). 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)..
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/610153
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