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Explore advanced concepts in disordered systems through this lecture delivered at the Bangalore School on Statistical Physics-XVI. Delve into the static and dynamic properties of systems with inherent randomness and disorder, examining how these characteristics influence physical behavior and phase transitions. Learn about theoretical frameworks used to analyze disordered materials, including random matrix theory, replica methods, and renormalization group techniques. Investigate the interplay between disorder and interactions in condensed matter systems, covering topics such as localization phenomena, spin glasses, and random walks in disordered media. Examine how disorder affects transport properties, critical behavior, and the emergence of complex phases in statistical mechanical systems. Gain insights into current research frontiers in the field, including applications to biological systems, optimization problems, and machine learning. This pedagogical presentation bridges the gap between master's-level statistical physics and cutting-edge research, making it valuable for PhD students, postdoctoral researchers, and faculty members working in theoretical physics and related fields.
