Explore stochastic vector computational approaches for electronic structure in extended condensed matter systems in this 55-minute lecture by Roi Baer from Hebrew University's Chemistry department. Discover how these methods reduce algorithmic complexity, enhance parallelization, simplify tasks, accelerate calculations, and minimize memory requirements. Examine the process of estimating electronic density through stochastic sampling of Kohn-Sham eigenstate contributions based on Fermi-Dirac occupation, bypassing the need for direct eigenstate calculations. Delve into post-DFT stochastic methods, including the G0W0 approximation for quasiparticle energies, presented at IPAM's Model Reduction in Quantum Mechanics Workshop on April 11, 2022.