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Explore concentration inequalities, a fundamental tool in probability and asymptotic geometric analysis, in this 48-minute lecture by Radek Adamczak. Delve into the softer approach to concentration based on functional inequalities, focusing on classical inequalities such as the Poincaré inequality and the log-Sobolev inequality. Examine their common properties, including tensorization, and discover how they lead to various forms of concentration for Lipschitz functions. Begin with the continuous setting, covering exponential and Gaussian measures, before progressing to discrete examples. If time allows, investigate concentration results for non-Lipschitz functions derived from functional inequalities. Gain insights into this essential topic that underpins limit theorems and existential results in high dimensions.
