11 papers
Gaussian Matrices and Exterior Forms: Deterministic Principal Ideals
Guangqian Zhao
For an infinite Gaussian matrix with independent entries and doubly monotone variances, we identify its algebraic principal ideal by a deterministic shell profile. The exact bounde…
Sharp Weak-Trace Regularity of Stochastic Cross Integrals
Guangqian Zhao
We prove a sharp spatial regularity theorem for the Itô and Stratonovich cross integrals of continuous semimartingales in separable Hilbert spaces. Without global moment assumption…
Operational State Selection in Stochastic Analysis: The Least State for a Calibrated Quadratic Ito Program
Guangqian Zhao
We study the least stable state determined by a causal response program and its quantitative calibration. For nondominated families of continuous Hilbert-valued semimartingale laws…
Algebraic Transfer for Operator-Valued Gaussian Chaoses:Oriented Schatten Profiles and Singular Wick Multipliers
Guangqian Zhao
We develop an algebraic transfer calculus for the oriented Schatten profiles of kernels underlying operator-valued Gaussian chaoses. A dimension-free link inequality propagates pro…
A Singular Stochastic Wave--Klein--Gordon System with Rough Gaussian Forcing and Distinct Propagation Speeds
Guangqian Zhao
We construct spatially local paracontrolled solutions on for the stochastic wave--Klein--Gordon system \[ (\partial_t^2-c_{\mathrm{W}}^2Δ)u=uv+ξ_{\mathrm{W}},\qquad…
Localized Centered Second-Chaos Operator
Guangqian Zhao
We prove a localized continuous-frequency operator estimate for centered Gaussian chaoses of order two. The result applies to operator-valued centered second chaoses, including Wic…
Gaussian Operator Algebras: Observability, Reconstruction, and Microscopic Limits
Guangqian Zhao
We reconstruct Gaussian operator algebras from finite source-labelled observations, recovering coefficients, ordinary multiplication, and completion in independently specified Scha…
Random Tensor Estimates and Deterministic Diagonal Resolutions for Mixed Paracontrolled Operators
Guangqian Zhao
We prove an operator-level convergence theorem for the mixed paracontrolled blocks \[ T^{i;j,k}_Λ(w) =I_i\bigl(w<Ψ_{j,Λ}\bigr)\circΨ_{k,Λ} \] on \(\mathbb T^d\), under Fourier-diag…
Color--Phase Separation for Mixed Random Operators in Two-Speed Stochastic Klein--Gordon Systems
Guangqian Zhao
We study a two-component stochastic fractional Klein--Gordon system on the three-dimensional torus with fractional dispersion exponent \(α\), distinct propagation speeds, and a pur…
Quantitative Driver-Only Capacity Cores and Simultaneous Scalar Itô Flows
Guangqian Zhao
We construct quantitative compact raw-driver cores for the maximal nondominated class of laws under which the coordinate process is a scalar continuous local martingale satis…
Common Causal Itô Flows under Nondominated Martingale Laws: Capacity Cores and Robust Sensitivities
Guangqian Zhao
Let \(Ω=C_0([0,T];\mathbb R)\), and let \(\mathfrak M_Λ\) be the laws under which the coordinate process is a continuous square-integrable martingale satisfying \(\mathrm d\langle…