分形高斯网络的单图推断
Single-graph inference for fractal Gaussian networks
- School of Mathematics (Zhuhai), Sun Yat-Sen University（中山大学数学学院（珠海））
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究针对顶点位置未观测的几何图，分析分形高斯网络的高斯乘性混沌强度推断问题，推导了相关统计量的极限性质、风险界与总变差率，通过数值研究验证了参数细化等特性。
AI中文摘要：
我们研究了从一个顶点位置未被观测的几何图中推断高斯乘性混沌强度的问题。在平面模型中，边计数统计量具有分段确定性极限，在γ=1处存在转变；而度分位数在整个亚临界范围内可一致估计ν=γ²/2。分数矩给出了一致的有限样本风险界。在有限分辨率下，通用图包络可对具有未知泊松强度的连续参数盒进行校准检验，对于固定统计量，在自适应细化下可实现同时覆盖；对于固定划分上独立试点的大小-度残差，可实现条件覆盖。对于精确的周期FFT-像素近似，我们证明了退火空间Cox律与观测图律的显式总变差率，在每个紧亚临界范围0≤γ≤Γ<2上一致成立。该率允许强度随分辨率增长，并意味着在每个分辨率下重新校准后可实现一致渐近覆盖。数值研究检验了参数细化、残差校准和多分辨率稳定性。
英文摘要：
We study inference on the strength of Gaussian multiplicative chaos from one geometric graph with unobserved vertex positions. In the planar model, the edge-count statistic has a piecewise deterministic limit with a transition at $γ=1$, whereas degree quantiles consistently estimate $ν=γ^2/2$ throughout the subcritical range. Fractional moments give uniform finite-sample risk bounds. At finite resolution, common graph envelopes calibrate tests over continuous parameter boxes with unknown Poisson intensity. They give simultaneous coverage under adaptive refinement for a fixed statistic, and conditional coverage for an independently piloted size--degree residual on a fixed partition. For the exact periodic FFT--pixel approximation, we prove explicit total-variation rates for the annealed spatial Cox law and the observed graph law, uniformly on every compact subcritical range $0\leγ\leΓ<2$. The rates allow intensity to grow with resolution and imply uniform asymptotic coverage after recalibration at each resolution. Numerical studies examine parameter refinement, residual calibration, and multiresolution stability.
