Szegö Type Limit Theorems

Szegö limit theorems for operators with almost periodic diagonals Steffen

The classical Szegö theorems study the asymptotic behaviour of the determinants of the finite sections PnT (a)Pn of Toeplitz operators, i.e., of operators which have constant entries along each diagonal. We generalize these results to operators which have almost periodic functions on their diagonals.

From Fibonacci numbers to central limit type theorems

A beautiful theorem of Zeckendorf states that every integer can be written uniquely as a sum of non-consecutive Fibonacci numbers {Fn}n=1. Lekkerkerker proved that the average number of summands for integers in [Fn, Fn+1) is n/(φ 2+1), with φ the golden mean. This has been generalized to the following: given nonnegative integers c1, c2, . . . , cL with c1, cL > 0 and recursive sequence {Hn}n=1 ...

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.