1 Abstract A complex quantum system with energy dissipation is considered. The quantum Hamilto-nians H belong the complex Ginibre ensemble. The complex-valued eigenenergies Z i are random variables. The second differences ∆ 1 Z i are also complex-valued random variables. The second differences have their real and imaginary parts and also radii (moduli) and main arguments (angles). For N=3 dimen...

The paper studies distribution of sum random processes from Orlicz spaces exponential type weighted by continuous functions, in particular, Subϕ (Ω), SSubϕ (Ω) and class V (ϕ, ψ) are considered. Such classes variables corresponding stochastic provide generalizations Gaussian sub-Gaussian important for various applications, example, queuing theory financial mathematics. We derive the estimates s...

This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many loss functions besides the squared loss, and scales only with the sub-Gaussian or subexponential parameters without further statistical assumptions such as the...

A number of basic properties about circularly-symmetric Gaussian random vectors are stated and proved here. These properties are each probably well known to most researchers who work with Gaussian noise, but I have not found them stated together with simple proofs in the literature. They are usually viewed as too advanced or too detailed for elementary texts but are used (correctly or incorrect...

A Gaussian polytope is the convex hull of normally distributed random points in a Euclidean space. We give an improved error bound for the expected number of facets of a Gaussian polytope when the dimension of the space is fixed and the number of points tends to infinity. The proof applies the theory of the asymptotic distribution of the top order statistic of a collection of independently dist...

Hierarchical mixed models are used to account for dependence between correlated data, in particular dependence created by a group structure within the sample. In such models, the correlation between observations is modelled by including, in the regression model, group-indexed parameters regarded as random variables, so called random eeects. Gaussian distributions are commonly used for the rando...

This technical report summarizes a number of results for the multivariate t distribution which can exhibit heavier tails than the Gaussian distribution. It is shown how t random variables can be generated, the probability density function (pdf) is derived, and marginal and conditional densities of partitioned t random vectors are presented. Moreover, a brief comparison with the multivariate Gau...

We show the existence of Gaussian multipartite bound information which is a classical analog of Gaussian multipartite bound entanglement. We construct a tripartite Gaussian distribution from which no secret key can be distilled between any two parties yet it cannot be created by local operations and public communication. This demonstrates a close link between entanglement and secrecy in the dom...

The spectral formulation of the stochastic nite element method (SSFEM) is applied to the problem of heat conduction in a random medium. Speciically, the conductivity of the medium, as well as its heat capacity are treated as uncorrelated random processes with spatial random uctuations. The paper introduces the basic concepts of the SSFEM using a simple one-dimensional heat conduction examples. ...