A Tight Bound on Localization of Electrical Flows
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911710654234624 |
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| author | Gurel-Gurevich, Ori Nachmias, Asaf Sachdeva, Sushant |
| author_facet | Gurel-Gurevich, Ori Nachmias, Asaf Sachdeva, Sushant |
| contents | We prove that for any unweighted graph on n vertices the L1 norm of a unit electric current between the endpoints of a random edge is at most 2 log n. Furthermore, we show that on any weighted graph the spectral norm of the entry-wise absolute value of the symmetric transfer-current matrix is at most 2 log n. This bound is tight up to constants and improves the O(log^2 n) bound from [Schild-Rao-Srivastava, SODA '18]. The initial proofs were generated by OpenAI's ChatGPT 5.5 Pro; the authors have verified and rewritten them to enhance readability and provide additional context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24130 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Tight Bound on Localization of Electrical Flows Gurel-Gurevich, Ori Nachmias, Asaf Sachdeva, Sushant Data Structures and Algorithms Discrete Mathematics Probability We prove that for any unweighted graph on n vertices the L1 norm of a unit electric current between the endpoints of a random edge is at most 2 log n. Furthermore, we show that on any weighted graph the spectral norm of the entry-wise absolute value of the symmetric transfer-current matrix is at most 2 log n. This bound is tight up to constants and improves the O(log^2 n) bound from [Schild-Rao-Srivastava, SODA '18]. The initial proofs were generated by OpenAI's ChatGPT 5.5 Pro; the authors have verified and rewritten them to enhance readability and provide additional context. |
| title | A Tight Bound on Localization of Electrical Flows |
| topic | Data Structures and Algorithms Discrete Mathematics Probability |
| url | https://arxiv.org/abs/2605.24130 |