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Vertex electrical model: Lagrangian and nonnegativity properties

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Abstract

We construct an embedding of the space of electrical networks to the totally nonnegative Lagrangian Grassmannian in a generic situation with the help of the technique of vertex integrable models of statistical mechanics.

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Acknowledgments

I am grateful to B. Bychkov, V. Gorbunov, and A. Kazakov for numerous discussions and especially to B. Bychkov for a careful reading of the text.

Funding

The work was partially supported by the “Basis” Science Foundation, the grant “Leader” (Math) 20-7-1-21-1 and the RFBR grant 20-01-00157A. This work was carried out within the framework of a development program for the Regional Scientific and Educational Mathematical Center of the Demidov Yaroslavl State University with financial support from the Ministry of Science and Higher Education of the Russian Federation (Agreement on provision of subsidy from the federal budget No. 075-02-2021-1397).

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    D. V. Talalaev

  2. Center of Integrable Systems, Demidov Yaroslavl State University, Yaroslavl, Russia

    D. V. Talalaev

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  1. D. V. Talalaev
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Correspondence to D. V. Talalaev.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2022, Vol. 210, pp. 250-258 https://doi.org/10.4213/tmf10188.

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Talalaev, D.V. Vertex electrical model: Lagrangian and nonnegativity properties. Theor Math Phys 210, 216–223 (2022). https://doi.org/10.1134/S0040577922020052

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  • DOI: https://doi.org/10.1134/S0040577922020052

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