We study simultaneous inference for maxima of canonical order-two $U$-statistics in high dimension. Degeneracy makes quadratic fluctuations leading, so ordinary Gaussian calibration can fail even after exact variance normalization. We show that the appropriate general target is a joint signed Gaussian quadratic chaos and establish a general approximation result that permits indefinite kernels. The general anti-concentration bound is too crude for high-dimensional inference, and we obtain sharper bounds under additional spectral structure. We also identify a phase transition from a non-Gaussian signed-chaos maximum to its covariance-matched Gaussian counterpart driven by the effective rank. For feasible inference, we propose a Gaussian multiplier bootstrap that avoid estimating eigensystems, and establish its validity. Two applications and extensive numerical simulations further illustrate the scope and practical performance of the proposed framework.
We study high-dimensional random-matrix limits of Gaussian Kullback--Leibler unbalanced optimal transport (KL-UOT). Under equal marginal penalties, the covariance action admits an exact log-determinant representation in terms of a nonlinear ridge product, together with a positive-semidefinite extension that remains fin...
We develop a Gaussian comparison theory for posterior inference in non-Gaussian high-dimensional models. The framework allows for model misspecification and does not require the posterior distribution itself to be approximately Gaussian. Working directly with likelihood processes on separable function spaces, we establ...
We study moderate deviations for the largest eigenvalue of the randomly deformed Gaussian unitary ensemble introduced by Johansson (Probab. Theory Relat. Fields, {\bf 138}: 75--112, 2007). In the fixed-coupling regime, the rescaled largest eigenvalue converges to the convolution of the Tracy--Widom law and a Gaussian l...
We develop an exact finite-perturbation response theory for the higher-order statistics of general state observables in nonequilibrium Markov networks. For local perturbations, the moment generating function obeys an exact nonlinear response identity in the perturbation strength, controlled by a single kinetic para...
Ruicheng Bao, Shiling Liang· Chinese Physics Letters· 0 citations
We study fixed-temperature logarithmic and Riesz gases after subtracting the leading mean-field contribution relative to a prescribed background law. For repulsive interactions in the Hilbert--Schmidt regime, we prove $N$-uniform bounds and quantitative convergence of the resulting modulated partition function to a nor...
M. G. Delgadino, Rishabh S. Gvalani, Matthew Rosenzweig· 2 citations
We introduce power variations of critical Gaussian multiplicative chaos (GMC) along refining partitions in arbitrary dimension. Under suitable renormalisation, we prove uniform fractional moment bounds via Laplace transform estimates as well as stable convergence to supercritical GMCs. Together, these results provide a...
Mo Dick Wong· 0 citations
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