Vertex electrical model: lagrangian and non-negative properties

TL;DR

This paper introduces a novel embedding of electrical networks into the totally non-negative Lagrangian Grassmannian using techniques from vertex integrable models, expanding the mathematical understanding of electrical network models.

Contribution

It provides a new geometric embedding of electrical networks into the non-negative Lagrangian Grassmannian leveraging integrable models, extending prior work.

Findings

Successful embedding of electrical networks into the Grassmannian

Application of integrable models to electrical network analysis

Enhanced geometric understanding of electrical network spaces

Abstract

This note is a modest addition to the work arXiv:2109.13952. Here we construct an embedding of the space of electrical networks to the totally non-negative Lagrangian Grassmannian in a generic situation with the help of the technique of vertex integrable models of statistical mechanics.