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Anticoncentration of Complex Gaussian Hafnians
Abstract
Let G2n be a complex symmetric random matrix whose entries above the diagonal are independent standard circular complex Gaussians, and let Hn=haf(G2n). We prove the uniform shifted anticoncentration bound Pr ( | Hn/(√((2n−1)!!))−z | ≤ ε ) ≤ 2√(n/π) ε2 for every z∈ℂ and ε>0. This establishes a local anticoncentration property that supports hardness arguments for quantum advantage in Gaussian boson sampling.
Related
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BibTeX
@misc{pant2026anticoncentration,
title = {{Anticoncentration of Complex Gaussian Hafnians}},
author = {Priyanshu Pant},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35019},
eprint = {2609.35019},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35019},
}
RIS
TY - UNPB
TI - Anticoncentration of Complex Gaussian Hafnians
AU - Priyanshu Pant
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35019
UR - https://arxiv.org/abs/2609.35019
AB - Let G_2n be a complex symmetric random matrix whose entries above the diagonal are independent standard circular complex Gaussians, and let H_n=haf(G_2n). We prove the uniform shifted anticoncentration bound Pr ( | H_n/(√((2n−1)!!))−z | ≤ ε ) ≤ 2√(n/π) ε^2 for every z∈ℂ and ε>0. This establishes a local anticoncentration property that supports hardness arguments for quantum advantage in Gaussian boson sampling.
ER -