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PreprintarXiv licencearXiv

Flow decomposition and stochastic completeness of weighted graphs

  • Qingsong Gu
  • Lu Hao
  • Xueping Huang
  • Yuhua Sun
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Abstract

We give a new proof by flow decomposition of the known Grigor'yan type integral criterion for stochastic completeness of weighted graphs. The main ingredient is a finite-domain estimate relating the mass of a killed $1$-resolvent and the current reaching the boundary to relative capacities of intrinsic balls. This estimate yields logarithmic criteria in terms of capacity to infinity and relative capacity, and recovers the volume criterion by an intrinsic cutoff, without passing to a metric graph or refining the graph.

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Cite

BibTeXRIS
BibTeX
@misc{gu2026flow,
  title = {{Flow decomposition and stochastic completeness of weighted graphs}},
  author = {Qingsong Gu and Lu Hao and Xueping Huang and Yuhua Sun},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26138},
  eprint = {2609.26138},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26138},
}
RIS
TY  - UNPB
TI  - Flow decomposition and stochastic completeness of weighted graphs
AU  - Qingsong Gu
AU  - Lu Hao
AU  - Xueping Huang
AU  - Yuhua Sun
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.26138
UR  - https://arxiv.org/abs/2609.26138
AB  - We give a new proof by flow decomposition of the known Grigor'yan type integral criterion for stochastic completeness of weighted graphs. The main ingredient is a finite-domain estimate relating the mass of a killed $1$-resolvent and the current reaching the boundary to relative capacities of intrinsic balls. This estimate yields logarithmic criteria in terms of capacity to infinity and relative capacity, and recovers the volume criterion by an intrinsic cutoff, without passing to a metric graph or refining the graph.
ER  -