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arXiv · 2609.35019

Anticoncentration of Complex Gaussian Hafnians

Priyanshu Pant
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Abstract

Let $G_{2n}$ be a complex symmetric random matrix whose entries above the diagonal are independent standard circular complex Gaussians, and let $H_n=\operatorname{haf}(G_{2n})$. We prove the uniform shifted anticoncentration bound $$ \Pr\!\left( \left| \frac{H_n}{\sqrt{(2n-1)!!}}-z \right| \le \varepsilon \right) \le 2\sqrt{\frac nπ}\,\varepsilon^2 $$ for every $z\in\mathbb C$ and $\varepsilon>0$. This establishes a local anticoncentration property that supports hardness arguments for quantum advantage in Gaussian boson sampling.

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Priyanshu Pant. 2026-09-28. Anticoncentration of Complex Gaussian Hafnians. https://arxiv.org/abs/2609.35019

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