[Algebra and Analysis Seminar]
Martin Burger (Westfälische Wilhelms-Universität Münster)
Gradient Structures for Graph PDEs and Limiting Procedures
PDE techniques for functions on finite graphs have become popular recently due to a variety of applications ranging from data science over social behaviour to biological networks. In this talk we will focus on the understanding of equations on finite graphs embedded in a Euclidean space and their continuum limits. First of all we will discuss gradient flow structures for graph PDEs, including recent findings for Markov chains. We will also show how to adapt the latter to many particle systems and their mean field limits.
In the second part of the talk we will give a preliminary discussion on how to obtain a structured limit of such embedded graphs, when the sampling of nodes, e.g. from some probability distribution, and correspondingly the number of edges increases. We will distinguish a regular graph limit, leading to nonlocal PDEs, and a singular limit leading to classical PDEs.
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