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arXiv · 2609.31200

Dirac measures can be quantum limits on the Sierpinski gasket

Patricia Alonso Ruiz·Nikolay Tzvetkov
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Abstract

We prove that on the Sierpinski gasket, a prototype of compact fractal space, Dirac distributions arise as the weak limit of probability measures associated with sequences of high energy eigenfunctions of the Laplacian in a way that cannot happen in compact Riemannian manifolds.

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Patricia Alonso Ruiz, Nikolay Tzvetkov. 2026-09-25. Dirac measures can be quantum limits on the Sierpinski gasket. https://arxiv.org/abs/2609.31200

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