Mathematical Sciences: Exponents and Symmetries of Operator-Stable Laws

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The principal investigator studies limit theorems for independent, identically distributed random vectors. In particular he will focus on the more tractable case of operator- stable random vectors. He plans to characterize associated symmetry groups of operator-stable laws. Limit theorems for sums of independent random variables are the foundation of mathematical statistics. In more than one dimension the corresponding analysis focuses on limit theorems for sums of independent random vectors. The principal investigator will investigate the specific case of the operator- stable class of probability laws.