Related papers: Discrete Gaussian distributions via theta function…
We study theta functions of a Riemann surface of genus g from the view point of tau function of a hierarchy of soliton equations. We study two kinds of series expansions. One is the Taylor expansion at any point of the theta divisor. We…
Gaussian comparison inequalities provide a way of bounding probabilities relating to multivariate Gaussian random vectors in terms of probabilities of random variables with simpler correlation structures. In this paper, we establish the…
We establish the meromorphic continuation of certain multiple zeta functions of generalized Hurwitz type. From this meromorphic continuation, we obtain explicit formulas for their (derivative) values at nonpositive integers along a given…
This paper proposes a novel method for testing observability in Gaussian models using discrete density approximations (deterministic samples) of (multivariate) Gaussians. Our notion of observability is defined by the existence of the…
We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…
Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian $\alpha$-stable distribution received much interest in…
The envelope of an elliptical Gaussian complex vector, or equivalently, the amplitude or norm of a bivariate normal random vector has application in many weather and signal processing contexts. We explicitly characterize its distribution in…
We compute the probability distribution of the interface width at the depinning threshold, using recent powerful algorithms. It confirms the universality classes found previously. In all cases, the distribution is surprisingly well…
We recall how the Gauss-Bonnet theorem can be interpreted as a finite dimen- sional index theorem. We describe the construction given in hep-th/0512293 of a function that can be interpreted as a gravitational effective action on a…
The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaussianity implies the finite dimensional distributions to be completely specified by the…
We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
Advection of a passive scalar $\theta$ in $d=2$ by a large-scale velocity field rapidly changing in time is considered. The Gaussian feature of the passive scalar statistics in the convective interval was discovered in \cite{95CFKLa}. Here…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
The individual terms of the series representing the Riemann zeta function are examined geometrically from their accumulated plot in the complex plane. Symmetry is identified and determined mathematically for comparison with more traditional…
We further develop the asymptotic analytic approach to the study of scattering diagrams. We do so by analyzing the asymptotic behavior of Maurer-Cartan elements of a differential graded Lie algebra constructed from a (not-necessarily…
We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…
The existence and uniqueness of the stationary distribution of the numerical solution generated by the stochastic theta method is studied. When the parameter theta takes different values, the requirements on the drift and diffusion…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
Chaudhry and Qadir obtained new identities for the gamma function by using a distributional representation for it. Here we obtain new identities for the Riemann zeta function and its family by using that representation for them. This also…