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Explore quantum fluctuations in two-dimensional fermionic systems through the lens of random matrix theory in this comprehensive lecture delivered at the International Centre for Theoretical Sciences. Delve into the mathematical frameworks that connect quantum many-body physics with statistical mechanics, examining how random matrix theory provides powerful tools for understanding fluctuation phenomena in 2D fermionic systems. Learn about the theoretical foundations linking quantum field theory, statistical mechanics, and matrix models in the context of nonequilibrium thermodynamics. Discover how these mathematical approaches illuminate the behavior of quantum systems far from equilibrium and their connections to classical statistical physics. Gain insights into cutting-edge research methodologies that bridge quantum mechanics and statistical theory, particularly relevant for understanding thermalization, transport phenomena, and fluctuation statistics in low-dimensional quantum systems. This presentation forms part of a broader program examining hydrodynamics, fluctuations, and noise across quantum and classical systems, offering perspectives on how different theoretical frameworks converge to describe nonequilibrium phenomena.
