A functional limit theorem for the profile of search trees

We study the profile $X_{n,k}$ of random search trees including binary search trees and $m$-ary search trees. Our main result is a functional limit theorem of the normalized profile $X_{n,k}/\mathbb{E}X_{n,k}$ for $k=\lfloor\alpha\log n\rfloor$ in a certain range of $\alpha$. A central feature of the proof is the use of the contraction method to prove convergence in distribution of certain random analytic functions in a complex domain. This is based on a general theorem concerning the contraction method for random variables in an infinite-dimensional Hilbert space. As part of the proof, we show that the Zolotarev metric is complete for a Hilbert space.Comment: Published in at http://dx.doi.org/10.1214/07-AAP457 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Higher Order Contact on Cayley's Ruled Cubic Surface

It is well known that Cayley's ruled cubic surface carries a three-parameter family of twisted cubics sharing a common point, with the same tangent and the same osculating plane. We report on various results and open problems with respect to contact of higher order and dual contact of higher order for these curves

How to make Dupire's local volatility work with jumps

There are several (mathematical) reasons why Dupire's formula fails in the non-diffusion setting. And yet, in practice, ad-hoc preconditioning of the option data works reasonably well. In this note we attempt to explain why. In particular, we propose a regularization procedure of the option data so that Dupire's local vol diffusion process recreates the correct option prices, even in manifest presence of jumps

and Navigation Group at DLR’s German Space Operations

member of the Executive and Governing Board of th

The KR System dlv: Progress Report, Comparisons and Benchmarks

dlv is a knowledge representation system, based on disjunctive logic programming, which offers frontends to several advanced KR formalisms. The system has been developed since one year at the Technical University of Vienna in an ongoing project funded by the Austrian Science Funds. After a report on the current state of the art in the implementation of dlv and of its application front-ends, the paper compares dlv with other knowledge representation systems. Both a qualitative and a quantitative comparison are carried out. The first compares the representational power of the systems (intended as the ability to represent problems in a natural and simple fashion). The latter compares the performances of the systems. The dlv system turns out to be very powerful from the knowledge representation side and, on the other hand, quite good also in computational power. Keywords: Implemented KR&R Systems: Reports, Comparisons, Evaluations. 1 INTRODUCTION The extension of logic programming by d..