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arXiv · 2610.17669

Large deviation principle for determinantal point processes on Stein manifolds

Kiyoon Eum
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Abstract

In this paper, we study natural determinantal point processes on Stein manifolds defined by canonical sections and plurisubharmonic weight functions. We present a natural condition on the weights under which these processes satisfy a large deviation principle with a good rate function given by the Fenchel--Legendre transform of the pluripotential equilibrium energy. Along the way, we prove some pluripotential theoretic results on Stein manifolds, such as the $C^{1,1}$ regularity of appropriate envelopes. These results are noncompact analogues of results of Berman and Berman--Boucksom on compact Kähler manifolds.

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Kiyoon Eum. 2026-10-13. Large deviation principle for determinantal point processes on Stein manifolds. https://arxiv.org/abs/2610.17669

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