On Gaussian random supergravity

Autoregressive Gaussian Random Vectors of First Order

On Dynamical Gaussian Random Walks

Motivated by the recent work of Benjamini, Häggström, Peres, and Steif (2003) on dynamical random walks, we: (i) Prove that, after a suitable normalization, the dynamical Gaussian walk converges weakly to the Ornstein–Uhlenbeck process in classical Wiener space; (ii) derive sharp tailasymptotics for the probabilities of large deviations of the said dynamical walk; and (iii) characterize (by way...

Random Gaussian sums on trees

Let T be a tree with induced partial order . We investigate centered Gaussian processes X = (X t)t∈T represented as X t = σ(t) ∑ v t α(v)ξv for given weight functions α and σ on T and with (ξv)v∈T i.i.d. standard normal. In a first part we treat general trees and weights and derive necessary and sufficient conditions for the a.s. boundedness of X in terms of compactness properties of (T, d). He...

On Expected Gaussian Random Determinants

The expectations of random determinants whose entries are real-valued, identically distributed, mean zero, correlated Gaussian random variables are examined using the Kronecker tensor products and some combinatorial arguments. This result is used to derive the expected determinants of X +B and AX +X ′B.

On the average number of sharp crossings of certain Gaussian random polynomials