# Laplacians on infinite graphs: discrete vs continuous

@inproceedings{Kostenko2021LaplaciansOI, title={Laplacians on infinite graphs: discrete vs continuous}, author={Aleksey Kostenko and Noema Nicolussi}, year={2021} }

There are two main notions of a Laplacian operator associated with graphs: discrete graph Laplacians and continuous Laplacians on metric graphs (widely known as quantum graphs). Both objects have a venerable history as they are related to several diverse branches of mathematics and mathematical physics. The existing literature usually treats these two Laplacian operators separately. In this overview, we will focus on the relationship between them (spectral and parabolic properties). Our main…

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