Description: Matched sampling, where the researcher first finds for each exposed unit (e.g., a smoker) a non-exposed unit (e.g., a never-smoker) who looks exactly like the exposed unit except for the exposure, and then compares outcomes (e.g., lung cancer rates) for the matched samples of units, is an intuitive method for inferring the causal effects of exposure versus non-exposure on the colle...
AbstractI will explain the solution to the following problem. Given a finite dimensional irreducible representation of a simple Lie algebra, consider its N-th tensor power. It has a decomposition into the direct sum of irreducible modules. The problem is how to find the asymptotic of multiplicities of irreducible subrepresentations in the limit N \to \infty and how to find the asymptotic of the...