@article{TMF_2022_210_2_a4,
author = {D. V. Talalaev},
title = {Vertex electrical model: {Lagrangian} and nonnegativity properties},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {250--258},
year = {2022},
volume = {210},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2022_210_2_a4/}
}
D. V. Talalaev. Vertex electrical model: Lagrangian and nonnegativity properties. Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 2, pp. 250-258. http://geodesic.mathdoc.fr/item/TMF_2022_210_2_a4/
[1] A. Postnikov, Total positivity, Grassmannians, and networks, arXiv: math/0609764
[2] P. Galashin, P. Pilyavskyy, “Ising model and the positive orthogonal Grassmannian”, Duke Math. J., 169:10 (2020), 1877–1942 | DOI | MR
[3] T. Lam, P. Pilyavskyy, “Electrical networks and Lie theory”, Algebra Number Theory, 9:6 (2015), 1401–1418 | DOI | MR
[4] T. Lam, “Electroid varieties and a compactification of the space of electrical networks”, Adv. Math., 338 (2018), 549–600 | DOI | MR
[5] S. Chepuri, T. George, D. E. Speyer, Electrical networks and Lagrangian Grassmannians, arXiv: 2106.15418
[6] B. Bychkov, V. Gorbounov, A. Kazakov, D. Talalaev, Electrical networks, Lagrangian Grassmannians and symplectic groups, arXiv: 2109.13952
[7] A. B. Zamolodchikov, “Uravneniya tetraedrov i integriruemye sistemy v trekhmernom prostranstve”, ZhETF, 79:2 (1980), 641–664 | MR
[8] S. Sergeev, chastnoe soobschenie, 2020
[9] V. Gorbounov, D. Talalaev, “Electrical varieties as vertex integrable statistical models”, J. Phys. A: Math. Theor., 53:45 (2020), 454001, 28 pp. | DOI | MR
[10] E. B. Curtis, D. Ingerman, J. A. Morrow, “Circular planar graphs and resistor networks”, Linear Algebra Appl., 283:1–3 (1998), 115–150 | DOI | MR
[11] E. B. Curtis, J. A. Morrow, Inverse Problems for Electrical Networks, Series on Applied Mathematics, 13, World Sci., Singapore, 2000 | DOI
[12] A. Berenstein, A. Gainutdinov, V. Gorbounov, chastnoe soobschenie, 2021