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arXiv · 1702.00466

Remarks on the thin obstacle problem and constrained Ginibre ensembles

Aram L. Karakhanyan
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Abstract

We consider the problem of constrained Ginibre ensemble with prescribed portion of eigenvalues on a given curve $\Gamma\subset \mathbb R^2$ and relate it to a thin obstacle problem. The key step in the proof is the $H^1$ estimate for the logarithmic potential of the equilibrium measure. The coincidence set has two components: one in $\Gamma$ and another one in $\mathbb R^2\setminus \Gamma$ which are well separated. Our main result here asserts that this obstacle problem is well posed in $H^1(\mathbb R^2)$ which improves previous results in $H^1_{loc}(\mathbb R^2)$.

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Aram L. Karakhanyan. 2017-02-01. Remarks on the thin obstacle problem and constrained Ginibre ensembles. https://arxiv.org/abs/1702.00466

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