Large deviations for random walks under subexponentiality: the big-jump domain

For a given one-dimensional random walk $\{S_n\}$ with a subexponential step-size distribution, we present a unifying theory to study the sequences $\{x_n\}$ for which $\mathsf{P}\{S_n>x\}\sim n\mathsf{P}\{S_1>x\}$ as $n\to\infty$ uniformly for $x\ge x_n$. We also investigate the stronger "local" analogue, $\mathsf{P}\{S_n\in(x,x+T]\}\sim n\mathsf{P}\{S_1\in(x,x+T]\}$. Our theory is self-contained and fits well within classical results on domains of (partial) attraction and local limit theory. When specialized to the most important subclasses of subexponential distributions that have been studied in the literature, we reproduce known theorems and we supplement them with new results.Comment: Published in at http://dx.doi.org/10.1214/07-AOP382 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

An evolution equation as the WKB correction in long-time asymptotics of Schrodinger dynamics

We consider 3d Schrodinger operator with long-range potential that has short-range radial derivative. The long-time asymptotics of non-stationary problem is studied and existence of modified wave operators is proved. It turns out, the standard WKB correction should be replaced by the solution to certain evolution equation.Comment: This is a preprint of an article whose final and definitive form has been published in Comm. Partial Differential Equations, available online at http://www.informaworld.co

Summary of the Very Large Hadron Collider Physics and Detector Subgroup

We summarize the activity of the Very Large Hadron Collider Physics and Detector subgroup during Snowmass 96.Comment: To appear in the Proceedings of the 1996 DPF/DPB Summer Study on New Directions for High-Energy Physics, Snowmass 9

Probing the deuteron structure at small NN distances by antiproton-deuteron annihilation

The production of pions by antiproton-deuteron annihilation at rest is analyzed. Assuming the possible existence of two delta-isobars in a deuteron some enhancement in the distribution over the invariant mass of two negative charged pions is predicted.Comment: 12 pages, Latex and Postscrip

Comment on "Coherent Ratchets in Driven Bose-Einstein Condensates"

C. E. Creffield and F. Sols (Phys. Rev. Lett. 103, 200601 (2009)) recently reported finite, directed time-averaged ratchet current, for a noninteracting quantum particle in a periodic potential even when time-reversal symmetry holds. As we explain in this Comment, this result is incorrect, that is, time-reversal symmetry implies a vanishing current.Comment: revised versio