3 papers
math.SP2025
Sums of projections with random coefficients
Leonid Pastur, Alexander Pushnitski
We study infinite sums \[ {\mathcal P}_{\varkappa}=\sum_{n=-\infty}^\infty \varkappa_n \langle\cdot, ψ_n\rangleψ_n \] of rank-one projections in a Hilbert space, where $\{ψ_n\}_{n\…
math.SP2025
Ergodic Hankel operators
Leonid Pastur, Alexander Pushnitski
We introduce a new class of operators: ergodic families of self-adjoint Hankel operators realised as integral operators on the half-line. Inspired by the spectral theory of differe…
math-ph2015
On the Equilibrium State of a Small System with Random Matrix Coupling to Its Environment
Joel L. Lebowitz, Leonid Pastur
We consider a random matrix model of interaction between a small -level system, , and its environment, a -level heat reservoir, . The interaction between and is…