[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematical Physics

arXiv:2502.16710 (math-ph)
[Submitted on 23 Feb 2025]

Title:Inverse problems related to electrical networks and the geometry of non-negative Grassmannians

Authors:A. A. Kazakov
View PDF HTML (experimental)
Abstract:In this paper we provide a new solution of the classical black box problem (the discrete Calderon problem) in the theory of circular electrical networks. Our approach is based on the explicit embedding of electrical networks into non-negative Grassmannians and generalized chamber ansatz for it. Additionally, we reveal the relationship of this problem with combinatorial properties of spanning groves and the theory of the totally non-negative matrices.
Key words: electrical networks, discrete Calderon problem, discrete electrical impedance tomography, non-negative Grassmannians, twist for positroid variety, Temperley trick, totally non-negative matrices, effective resistances.
Subjects: Mathematical Physics (math-ph); Analysis of PDEs (math.AP)
MSC classes: 05C10, 05C50, 05E10, 15M15, 34B45, 35R30, 82B20, 90C05, 90C59, 94C05, 94C15
Cite as: arXiv:2502.16710 [math-ph]
  (or arXiv:2502.16710v1 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.2502.16710

Submission history

From: Anton Kazakov [view email]
[v1] Sun, 23 Feb 2025 20:49:56 UTC (3,875 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math-ph
< prev   |   next >
new | recent | 2025-02
Change to browse by:
math
math.AP
math.MP

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)