Monte Carlo methods on compact symplectic manifolds

Yuri A. Kordyukov

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arXiv · 2608.07021

Monte Carlo methods on compact symplectic manifolds

Yuri A. Kordyukov

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Abstract

We build an unbiased Monte Carlo estimator of the integral of any $C^1$ function on a prequantized compact symplectic manifold against a smooth Riemannian volume form, taking for quadrature nodes the determinantal point process associated with an appropriate spectral projection of the Bochner-Schr\"odinger operator. We show that the estimator satisfies a central limit theorem, and the decay rate of the mean squared error reaches the optimal worst-case rate investigated by Bakhvalov in Euclidean spaces. These results extend previous results of Lemoine and Bardenet on Monte Carlo methods on compact complex manifolds.

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BibTeX RIS

Yuri A. Kordyukov. 2026-08-07. Monte Carlo methods on compact symplectic manifolds. https://arxiv.org/abs/2608.07021

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