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Moments of Gaussian chaoses in Banach spaces
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Moments of Gaussian chaoses in Banach spaces
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We derive moment and tail estimates for Gaussian chaoses of arbitrary order with values in Banach spaces. We formulate a conjecture regarding two-sided estimates and show that it holds in a certain class of Banach spaces including L_q spaces. As a corollary we obtain two-sided bounds for moments of chaoses with values in L_q spaces based on exponential random variables.
Forward citations
Cited by 4 Pith papers
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Schatten-Class Wick Multipliers for Gaussian Fields on Closed Riemannian Manifolds: Oriented Tensor Estimates and Covariance-Profile Transfer
Establishes that the L^p(Ω; S_r) norm of a finite-order decoupled homogeneous Gaussian chaos operator is bounded by C_m (p+r)^{m/2} times the maximum oriented Schatten flattening norm of its kernel.
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Schatten-Class Wick Multipliers for Gaussian Fields on Closed Riemannian Manifolds: Oriented Tensor Estimates and Covariance-Profile Transfer
Fixed-order Hilbertian Gaussian chaos operators satisfy ||T_K^{(m)}||_{L^p S_r} ≤ C_m (p+r)^{m/2} max_S ||F_S(K)||_{S_r}, with constants independent of Hilbert dimensions and cutoff ranks.
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Schatten-Class Wick Multipliers for Gaussian Fields on Closed Riemannian Manifolds: Oriented Tensor Estimates and Covariance-Profile Transfer
Fixed-order Hilbertian Gaussian chaoses satisfy ||T_K^{(m)}||_{L^p S_r} ≤ C_m (p+r)^{m/2} max_S ||F_S(K)||_{S_r}, with completion, Wick, and cutoff-Cauchy consequences.
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Schatten-Class Wick Multipliers for Gaussian Fields on Closed Riemannian Manifolds: Oriented Tensor Estimates and Covariance-Profile Transfer
A finite-order Gaussian chaos estimate converts deterministic Schatten flattening bounds into dimension-free moment, tail, and convergence estimates for operator-valued random tensors.
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