We study the characteristic function and moments of the integer-valued random variable X+α , where X is a continuous random variables. The results can be regarded as exact versions of Sheppard’s correction. Rounded variables of this type often occur as subsequence limits of sequences of integer-valued random variables. This leads to oscillatory terms in asymptotics for these variables, somethin...

A complex quantum system with energy dissipation is considered. The quantum Hamiltonians H belong the complex Ginibre ensemble. The complex-valued 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). For N=3 dimensional Ginibre en...

A complex quantum system with energy dissipation is considered. The quantum Hamiltonians H belong the complex Ginibre ensemble. The complex-valued 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). For N=3 dimensional Ginibre en...