Related papers: Gaussian vectors with Markov property
Recent research has shown the potential utility of Deep Gaussian Processes. These deep structures are probability distributions, designed through hierarchical construction, which are conditionally Gaussian. In this paper, the current…
This short expository paper outlines applications of computer algebra to the implication problem of conditional independence for Gaussian random variables. We touch on certificates for validity and invalidity of inference rules from the…
This thesis reviews recent progress on products of random matrices from the perspective of exactly solved Gaussian random matrix models. We derive exact formulae for the correlation functions for the eigen- and singular values at arbitrary…
In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…
We provide a new and simple characterization of the multivariate generalized Laplace distribution. In particular, this result implies that the product of a Gaussian matrix with independent and identically distributed columns by an…
We construct "stochastic mappings" between power law probability distributions (PD's) and Gaussian ones. To a given vector $N$, Gaussian distributed (respectively $Z$, exponentially distributed), one can associate a vector $X$, "power law…
This paper discusses the family of distributions on the Grassmannian of the linear span of r central gaussian vectors parametrized by the covariance matrix. Our main result is an existence and uniqueness criterion for the maximum likelihood…
Let $\{X_i(t),t\ge0\}, 1\le i\le n$ be mutually independent centered Gaussian processes with almost surely continuous sample paths. We derive the exact asymptotics of $$ P\left(\exists_{t \in [0,T]} \forall_{i=1 ... n} X_i(t)> u \right) $$…
The space of Gaussian measures on a Euclidean space is geodesically convex in the $L^2$-Wasserstein space. This space is a finite dimensional manifold since Gaussian measures are parameterized by means and covariance matrices. By…
We study the eigenvalues and the eigenvectors of $N\times N$ structured random matrices of the form $H = W\tilde{H}W+D$ with diagonal matrices $D$ and $W$ and $\tilde{H}$ from the Gaussian Unitary Ensemble. Using the supersymmetry technique…
The starting point of this work is a theorem due to Maxwell characterizing the distribution of a Gaussian vector with at least two coordinates. We define the Gaussian orthogonal, unitary and symplectic tensor ensembles for notions of real…
We prove a dimension-free tail comparison between the Euclidean norms of sums of independent random vectors uniformly distributed in centred Euclidean spheres and properly rescaled standard Gaussian random vectors.
We show that any quantum density matrix can be represented by a Bayesian network (a directed acyclic graph), and also by a Markov network (an undirected graph). We show that any Bayesian or Markov net that represents a density matrix, is…
We study singularities of Gauss maps of fronts and give characterizations of types of singularities of Gauss maps by geometric properties of fronts which are related to behavior of bounded principal curvatures. Moreover, we investigate…
This paper presents the Gaussian subordination framework to generate optimal one-sided approximations to multidimensional real-valued functions by functions of prescribed exponential type. Such extremal problems date back to the works of…
We discuss the Pistone-Sempi exponential manifold on the finite-dimensional Gaussian space. We consider the role of the entropy, the continuity of translations, Poincar\'e-type inequalities, the generalized differentiability of probability…
We introduce an $\ell$-adic analogue of Gauss's hypergeometric function arising from the Galois action on the fundamental torsor of the projective line minus three points. Its definition is motivated by a relation between the KZ-equation…
We investigate the sub-Gaussian property for almost surely bounded random variables. If sub-Gaussianity per se is de facto ensured by the bounded support of said random variables, then exciting research avenues remain open. Among these…
We establish a strong Gaussian approximation for high-dimensional non-degenerate U-statistics with diverging dimension. Under mild assumptions, we construct, on a sufficiently rich probability space, a Gaussian process that uniformly…
We employ the ergodic theoretic machinery of scenery flows to address classical geometric measure theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely…