Operator limit theorems

Entropy and Limit Theorems

I hereby declare that my thesis entitled`Entropy and Limit Theo-rems' is not substantially the same as any that I have submitted for a degree or diploma or other qualiication at any other University. I further state that no part of my thesis has already been or is being concurrently submitted for any such degree, diploma or other qualiication. Chapter 3 extends results from a paper co-written w...

Some Limit Theorems

Limit theorems for mergesort

Central and local limit theorems (including large deviations) are established for the number of comparisons used by the standard top-down recursive mergesort under the uniform permutation model. The method of proof utilizes Dirichlet series, Mellin transforms and standard analytic methods in probability theory.

Szegő Limit Theorems

The first Szegő limit theorem has been extended by Bump-Diaconis and Tracy-Widom to limits of other minors of Toeplitz matrices. We extend their results still further to allow more general measures and more general determinants. We also give a new extension to higher dimensions, which extends a theorem of Helson and Lowdenslager. §

Nonconventional Limit Theorems

The polynomial ergodic theorem (PET) which appeared in [1] and attracted substantial attention in ergodic theory studies the limits of expressions having the form 1/N ∑n=1 T q1(n) f1 · · ·T ql(n) fl where T is a weakly mixing measure preserving transformation, fi’s are bounded measurable functions and qi’s are polynomials taking on integer values on the integers. Motivated partially by this res...