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math.SP2026
Dirac measures can be quantum limits on the Sierpinski gasket
Patricia Alonso Ruiz, Nikolay Tzvetkov
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…
math.PR2026
Towards Liouville Quantum Gravity on fractals
Patricia Alonso Ruiz, Eva Kopfer
Motivated by the recent construction of fractional Gaussian fields on the Sierpinski gasket, we study those Gaussian fields whose covariance function exhibits a logarithmic behavio…