Related papers: Characterization of positively correlated squared …
The covariance function of a Gauss-Markov process evaluated at points $(s,t)$ admits a representation as a product of a function of $\min(s,t)$ and a function of $\max(s,t)$. We call these functions the covariance factors of a Gauss-Markov…
Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…
We study the probabilistic behaviour of the continued fraction expansion of a quadratic irrational number, when weighted by some "additive" cost. We prove asymptotic Gaussian limit laws, with an optimal speed of convergence. We deal with…
Two integrable random vectors $\xi$ and $\xi^*$ in $\mathbb {R}^d$ are said to be zonoid equivalent if, for each $u\in \mathbb {R}^d$, the scalar products $\langle\xi,u\rangle$ and $\langle\xi^*,u\rangle$ have the same first absolute…
We present a numerical method for solving the separability problem of Gaussian quantum states in continuous-variable quantum systems. We show that the separability problem can be cast as an equivalent problem of determining the feasibility…
We provide a geometric characterization of rigidity of equality cases in Ehrhard's symmetrization inequality for Gaussian perimeter. This condition is formulated in terms of a new measure-theoretic notion of connectedness for Borel sets,…
We show that for a wide class of Gaussian random fields, points are polar in the critical dimension. Examples of such random fields include solutions of systems of linear stochastic partial differential equations with deterministic…
Quadratic harnesses are time-inhomogeneous Markov polynomial processes with linear conditional expectations and quadratic conditional variances with respect to the past-future filtrations. Typically they are determined by five numerical…
A decoupling type inequality for a sum of functions of Guassian vectors is established.
Starting with the correspondence between positive definite kernels on the one hand and reproducing kernel Hilbert spaces (RKHSs) on the other, we turn to a detailed analysis of associated measures and Gaussian processes. Point of departure:…
This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations. Such equations involve, but are not limited to, ordinary and partial differential,…
Let $\Omega\subset\mathbb{R}^n$ be an open, connected subset of $\mathbb{R}^n$, and let $F\colon\Omega-\Omega\to\mathbb{C}$, where $\Omega-\Omega=\{x-y\colon x,y\in\Omega\}$, be a continuous positive definite function. We give necessary and…
We provide the strong approximation of empirical copula processes by a Gaussian process. In addition we establish a strong approximation of the smoothed empirical copula processes and a law of iterated logarithm.
We define epsilon factors for irreducible representations of finite general linear groups using Macdonald's correspondence. These epsilon factors satisfy multiplicativity, and are expressible as products of Gauss sums. The tensor product…
In all our well-established theories, it is assumed that events are embedded in a global causal structure such that, for every pair of events, the causal order between them is always fixed. However, the possible interplay between quantum…
Gaussian processes are a key component of many flexible statistical and machine learning models. However, they exhibit cubic computational complexity and high memory constraints due to the need of inverting and storing a full covariance…
We give generators and relations for the hypergraph props of Gaussian relations and positive affine Lagrangian relations. The former extends Gaussian probabilistic processes by completely-uninformative priors, and the latter extends…
The asymptotic analysis of high exceedance probabilities for Gaussian processes and fields has been a blooming research area since J. Pickands introduced the now-standard techniques in the late 60's. The \textit{vector-valued} processes,…
About forty years ago it was realized by several researchers that the essential features of certain objects of Probability theory, notably Gaussian processes and limit theorems, may be better understood if they are considered in settings…
The dynamical behavior of interacting systems plays a fundamental role for determining quantum correlations, such as entanglement. In this Letter, we describe temporal quantum effects of the inseparable evolution of composite quantum states…