Characteristic function of a multivariate normal law

Depends on

• Multivariate normal law, including singular covariance
• Characteristic function of a normal law
• Uniqueness of a law from its characteristic function
• Cramer wold device
• Characteristic function of a real random variable
• The Axiom of Choice

Used by

• Matching minimax rate in a Gaussian orthogonal sequence model Corollary
• Vector Levy characterization Corollary
• Two visits can alias random-slope and residual variance components Counterexample
• Canonical group-sequential alpha-spending design Definition
• Chi-square laws, including zero degrees Definition
• d-dimensional Brownian motion Definition
• The iid multivariate-normal sample and covariance conventions Definition
• Wishart law by Gaussian outer products Definition
• A degenerate multivariate Gaussian limit Example
• A hidden common cause is observationally indistinguishable from an edge Example
• An iid Gaussian cylinder process is not an ℓ²-valued prior Example
• Covariance of deterministic Ito integrals Example
• A deterministic Itô integral has independent Gaussian increments Lemma
• A finite stack of independent Gaussian vectors is jointly Gaussian Lemma
• A Gaussian error contrast has the induced multivariate-normal law Lemma
• Adjacent iid vector functionals admit a finite-moment strong approximation Lemma
• Bounded independent vector rows admit a logarithmic cubed Gaussian coupling Lemma
• Brownian covariance is equivalent to independent stationary normal increments Lemma
• Consistency of Brownian finite-dimensional laws Lemma
• Continuity of bivariate Gaussian feature expectations, including singular limits Lemma
• Endpoint law and restriction density of a scalar Brownian bridge Lemma
• Finite Sudakov–Fernique comparison for Gaussian maxima Lemma
• Finite-dimensional LAN convolution bound for differentiable functionals Lemma
• Gaussian anchored bounded sums have uniform cumulant and Fourier bounds Lemma
• Heterogeneous bounded atom vector rows admit a logarithmic cubed Gaussian coupling Lemma
• Invariant Gaussian law and uniqueness for a stable autoregression Lemma
• Jointly Gaussian blocks with zero cross-covariance are independent, including singular blocks Lemma
• Mean and covariance determine Gaussian finite-dimensional laws Lemma
• Moderate deviation density bounds for Gaussian anchored sums Lemma
• The pCN Gaussian reference pair law is symmetric Lemma
• Uncorrelated jointly Gaussian Banach random elements are independent Lemma
• Uncorrelated jointly Gaussian blocks are independent Lemma
• The limiting neural tangent kernel is strictly positive definite on every unit sphere Proposition
• Computational costs and limits of finite Gaussian-process regression Remark
• A mean and positive-semidefinite kernel define a Gaussian process Theorem
• A positive-definite multivariate normal law has its Gaussian density Theorem
• Borell concentration for the norm of a separable Banach Gaussian Theorem
• Cameron–Martin translation formula for a separable Banach Gaussian Theorem
• Convolution bound for regular estimators Theorem
• Exact increment laws in the dyadic Brownian bridge tree Theorem

…and 13 more results.

Dependency tree · two levels

51 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• Norris, Probability and Measure, Theorem 8.2.1 (standard reference, not scraped)
• Aldous and Chewi, Probability Theory notes, Theorem 8.2 (standard reference, not scraped)