# The effective impedances of infinite ladder networks and Dirichlet problem on graphs

@article{Muranova2020TheEI, title={The effective impedances of infinite ladder networks and Dirichlet problem on graphs}, author={Anna Muranova}, journal={arXiv: Combinatorics}, year={2020} }

We calculate effective impedances of infinite $LC$- and $CL$- ladder networks as limits of effective impedances of finite network approximations, using a new method, which involves precise mathematical concepts. These concepts are related to the classical differential operators on weighted graphs. As an auxiliary result, we solve a discrete boundary value Dirichlet problem on a finite ladder network.

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