Universität zu Köln

Drewitz, Alexander ORCID: 0000-0002-5546-3614, Prevost, Alexis and Rodriguez, Pierre-Francois ORCID: 0000-0001-7607-0724 (2023). Critical exponents for a percolation model on transient graphs. Invent. Math., 232 (1). S. 229 - 300. HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1432-1297

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Abstract

We consider the bond percolation problem on a transient weighted graph induced by the excursion sets of the Gaussian free field on the corresponding cable system. Owing to the continuity of this setup and the strong Markov property of the field on the one hand, and the links with potential theory for the associated diffusion on the other, we rigorously determine the behavior of various key quantities related to the (near-)critical regime for this model. In particular, our results apply in case the base graph is the three-dimensional cubic lattice. They unveil the values of the associated critical exponents, which are explicit but not mean-field and consistent with predictions from scaling theory below the upper-critical dimension.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Drewitz, Alexander UNSPECIFIED orcid.org/0000-0002-5546-3614 UNSPECIFIED Prevost, Alexis UNSPECIFIED UNSPECIFIED UNSPECIFIED Rodriguez, Pierre-Francois UNSPECIFIED orcid.org/0000-0001-7607-0724 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-671818
DOI:	10.1007/s00222-022-01168-z
Journal or Publication Title:	Invent. Math.
Volume:	232
Number:	1
Page Range:	S. 229 - 300
Date:	2023
Publisher:	SPRINGER HEIDELBERG
Place of Publication:	HEIDELBERG
ISSN:	1432-1297
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language GAUSSIAN FREE-FIELD; RENORMALIZATION-GROUP; INEQUALITIES; CLUSTERS; SYSTEMS; SET Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/67181