# Nonlocal quadratic forms with visibility constraint (joint work with Moritz Kassmann)

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FKT - Frontiers in kinetic theory: connecting microscopic to macroscopic scales - KineCon 2022

Given a subset $D$ of the Euclidean space, we study nonlocal quadratic forms that take into account tuples $(x, y) \in D \times D$ if and only if the line segment between $x$ and $y$ is contained in $D$. We discuss regularity of the corresponding Dirichlet form leading to the existence of a pure-jump process with visibility constraint. Our main aim is to investigate corresponding Poincar\’ e inequalities and their scaling properties. For dumbbell shaped domains we show that the forms satisfy a Poincar\’ e inequality with diffusive scaling.

This talk is part of the Isaac Newton Institute Seminar Series series.

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