PreprintCC BY-NC-SA 4.0arXiv
Quenched functional central limit theorem for the random conductance model under minimal moments
Abstract
We prove a quenched functional central limit theorem for the random conductance model with ergodic translation-invariant, strictly positive nearest-neighbor conductances, assuming only finite first moments of the conductances and their inverses. This settles an open problem by reaching the critical first-moment threshold, which is sharp for a certain class of integrability assumptions. A key ingredient of the proof is a new Sobolev inequality that seems to be missing from the literature.
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BibTeX
@misc{kolesnikov2026quenched,
title = {{Quenched functional central limit theorem for the random conductance model under minimal moments}},
author = {Leonid Kolesnikov and Yannic Steenbeck},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19751},
eprint = {2609.19751},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19751},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Quenched functional central limit theorem for the random conductance model under minimal moments
AU - Leonid Kolesnikov
AU - Yannic Steenbeck
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19751
UR - https://arxiv.org/abs/2609.19751
AB - We prove a quenched functional central limit theorem for the random conductance model with ergodic translation-invariant, strictly positive nearest-neighbor conductances, assuming only finite first moments of the conductances and their inverses. This settles an open problem by reaching the critical first-moment threshold, which is sharp for a certain class of integrability assumptions. A key ingredient of the proof is a new Sobolev inequality that seems to be missing from the literature.
ER -