Kim, Ji Hee2013-07-232013-07-232013-05https://hdl.handle.net/11299/153632University of Minnesota Ph.D. dissertation. May 2013. Major: Mathematics. Advisor: Sergey G. Bobkov. 1 computer file (PDF); ii, 65 pages, appendix A-B.The concentration property of empirical distribution functions is studied under the Levy distance for dependent data whose joint distribution satisfies analytic conditions expressed via Poincare-type and logarithmic Sobolev inequalities. The concentration results are then applied to the following two general schemes. In the first scheme, the data are obtained as coordinates of a point randomly selected within given convex bodies (and more generally -- when the sample obeys a log-concave distribution). In the second scheme, the data represent eigenvalues of symmetric random matrices whose entries satisfy the indicated analytic conditions.en-USConcentration of measureDependent dataEmpirical measureIsoperimetryProbabilityThesis or Dissertation