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Explore concentration inequalities, a fundamental tool in probability and asymptotic geometric analysis, in this 49-minute lecture by Radek Adamczak at the Hausdorff Center for Mathematics. Delve into the softest approach to concentration, focusing on functional inequalities such as the Poincaré inequality and log-Sobolev inequality. Examine their basic 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. Gain insights into concentration results for non-Lipschitz functions derived from functional inequalities, and understand the evolution of concentration estimate methods from isoperimetric inequalities to more accessible approaches applicable to broader measure classes.
