2 7 N ov 2 00 6 Log - concavity and LC - positivity

Log-concavity and LC-positivity

A triangle {a(n, k)}0≤k≤n of nonnegative numbers is LC-positive if for each r, the sequence of polynomials ∑n k=r a(n, k)q k is q-log-concave. It is double LC-positive if both triangles {a(n, k)} and {a(n, n − k)} are LC-positive. We show that if {a(n, k)} is LC-positive then the log-concavity of the sequence {xk} implies that of the sequence {zn} defined by zn = ∑n k=0 a(n, k)xk, and if {a(n, ...

N ov 2 00 6 SIMPLE MONTE CARLO AND THE METROPOLIS ALGORITHM

We study the integration of functions with respect to an unknown density. Information is available as oracle calls to the integrand and to the non-normalized density function. We are interested in analyzing the integration error of optimal algorithms (or the complexity of the problem) with emphasis on the variability of the weight function. For a corresponding large class of problem instances w...

N ov 2 00 2 AFFINE MANIFOLDS , LOG STRUCTURES , AND MIRROR SYMMETRY

N ov 2 00 6 A Kiefer Wolfowitz Comparison Theorem For Wicksell ’ s Problem

We extend the isotonic analysis for the Wicksell’s problem to estimate a regression function, which is motivated by the problem of estimating dark matter distribution in Astronomy. The main result is a version of the Kiefer-Wolfowitz theorem comparing the empirical distribution to its least concave majorant, but with a convergence rate n −1 log n faster than n−2/3 log n. The main result is usef...

ar X iv : h ep - t h / 01 11 18 6 v 1 2 1 N ov 2 00 1 1 Dynamical Zero Modes and Criticality in Continuous Light Cone Quantization of Φ 41 + 1

Critical behaviour of the 2D scalar field theory in the LC framework is reviewed. The notion of dynamical zero modes is introduced and shown to lead to a non trivial covariant dispersion relation only for Continuous LC Quantization (CLCQ). The critical exponent η is found to be governed by the behaviour of the infinite volume limit under conformal transformations properties preserving the local...