A complex quantum system with energy dissipation is considered. The quantum Hamiltonians H belong the complex Ginibre ensemble. The complexvalued eigenenergies Zi are random variables. The second differences ∆ Zi are also complex-valued random variables. The second differences have their real and imaginary parts and also radii (moduli) and main arguments (angles). ForN=3 dimensional Ginibre ens...

In this paper, we firstly introduce the definition of fuzzy metric sets, and discuss properties induced by Hausdorff metric. Then prove limit theorems for set-valued random variables in space; convergence is about The work an extension from classical results to space.

This set of notes will cover basic concepts in multivariate probability models, i.e., probability models involving multiple random variables. We will begin by discussing the important concepts of independence and conditional independence and then look at the general framework of graphical models. We will then look at specific examples of models: for joint distributions we will look at the naive...

We improve here two results from the preprints [DK], [AFKK] on approximating matrices by random submatrices. We use a construction of a random subset of a finite set, which is different from what was suggested in [AFKK]. Instead of taking a random q-element subset of an n-element set, we consider independent {0, 1}-valued random variables δ1, . . . , δn, taking value 1 with probability δ = q/n....