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In this talk, I provide an introduction to the Eigenstate Thermalisation Hypothesis (ETH) in the context of Random Matrix Theory (RMT) and discuss our most recent findings, which invalidate the inverse-density scaling of the ETH fluctuations, as put forward by Feingold and Peres in the 1980s and later incorporated into the celebrated Srednicki ansatz. Based on joint work with G. Cipolloni, L. Erdos, and V. Riabov.