Deviations of a random walk in a random scenery with stretched exponential tails

Let (Z_n)_{n\in\N_0} be a d-dimensional random walk in random scenery, i.e., Z_n=\sum_{k=0}^{n-1}Y_{S_k} with (S_k)_{k\in\N_0} a random walk in Z^d and (Y_z)_{z\in Z^d} an i.i.d. scenery, independent of the walk. We assume that the random variables Y_z have a stretched exponential tail. In particular, they do not possess exponential moments. We identify the speed and the rate of the logarithmic decay of Pr(Z_n>t_n n) for all sequences (t_n)_{n\in\N} satisfying a certain lower bound. This complements previous results, where it was assumed that Y_z has exponential moments of all orders. In contrast to the previous situation,the event \{Z_n>t_nn\} is not realized by a homogeneous behavior of the walk's local times and the scenery, but by many visits of the walker to a particular site and a large value of the scenery at that site. This reflects a well-known extreme behavior typical for random variables having no exponential moments.Comment: 12 page

Joint density for the local times of continuous-time Markov chains

We investigate the local times of a continuous-time Markov chain on an arbitrary discrete state space. For fixed finite range of the Markov chain, we derive an explicit formula for the joint density of all local times on the range, at any fixed time. We use standard tools from the theory of stochastic processes and finite-dimensional complex calculus. We apply this formula in the following directions: (1) we derive large deviation upper estimates for the normalized local times beyond the exponential scale, (2) we derive the upper bound in Varadhan's lemma for any measurable functional of the local times, and (3) we derive large deviation upper bounds for continuous-time simple random walk on large subboxes of $\mathbb{Z}^d$ tending to $\mathbb{Z}^d$ as time diverges. We finally discuss the relation of our density formula to the Ray--Knight theorem for continuous-time simple random walk on $\mathbb{Z}$, which is analogous to the well-known Ray--Knight description of Brownian local times.Comment: Published at http://dx.doi.org/10.1214/009171906000001024 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Aharonov-Bohm Interferometry with Interacting Quantum Dots: Spin Configurations, Asymmetric Interference Patterns, Bias-Voltage-Induced Aharonov-Bohm Oscillations, and Symmetries of Transport Coefficients

We study electron transport through multiply-connected mesoscopic geometries containing interacting quantum dots. Our formulation covers both equilibrium and non-equilibrium physics. We discuss the relation of coherent transport channels through the quantum dot to flux-sensitive Aharonov-Bohm oscillations in the total conductance of the device. Contributions to transport in first and second order in the intrinsic line width of the dot levels are addressed in detail. We predict an interaction-induced asymmetry in the amplitude of the interference signal around resonance peaks as a consequence of incoherence associated with spin-flip processes. This asymmetry can be used to probe the total spin of the quantum dot. Such a probe requires less stringent experimental conditions than the Kondo effect, which provides the same information. We show that first-order contributions can be partially or even fully coherent. This contrasts with the sequential-tunneling picture, which describes first-order transport as a sequence of incoherent tunneling processes. We predict bias-voltage induced Aharonov-Bohm oscillations of physical quantities which are independent of flux in the linear-response regime. Going beyond the Onsager relations we analyze the relations between the space symmetry group of the setup and the flux-dependent non-linear conductance.Comment: 22 pages, 11 figure

Large deviations for the one-dimensional Edwards model

Article / Letter to editorMathematisch Instituu

Weak interaction limits for one-dimensional random polymers

Analysis and Stochastic

Kondo Correlations and the Fano Effect in Closed AB-Interferometers

We study the Fano-Kondo effect in a closed Aharonov-Bohm (AB) interferometer which contains a single-level quantum dot and predict a frequency doubling of the AB oscillations as a signature of Kondo-correlated states. Using Keldysh formalism, Friedel sum rule and Numerical Renormalization Group, we calculate the exact zero-temperature linear conductance $G$ as a function of AB phase $\phi$ and level position $\epsilon$. In the unitary limit, $G(\phi)$ reaches its maximum $2e^2/h$ at $\phi=\pi/2$. We find a Fano-suppressed Kondo plateau for $G(\epsilon)$ similar to recent experiments.Comment: 4 pages, 4 eps figure

APECS - The Atacama Pathfinder Experiment Control System

APECS is the distributed control system of the new Atacama Pathfinder EXperiment (APEX) telescope located on the Llano de Chajnantor at an altitude of 5107 m in the Atacama desert in northern Chile. APECS is based on Atacama Large Millimeter Array (ALMA) software and employs a modern, object-oriented design using the Common Object Request Broker Architecture (CORBA) as the middleware. New generic device interfaces simplify adding instruments to the control system. The Python based observer command scripting language allows using many existing software libraries and facilitates creating more complex observing modes. A new self-descriptive raw data format (Multi-Beam FITS or MBFITS) has been defined to store the multi-beam, multi-frequency data. APECS provides an online pipeline for initial calibration, observer feedback and a quick-look display. APECS is being used for regular science observations in local and remote mode since August 2005.Comment: 4 pages, A&A, accepte

A SOA-based architecture framework

We present an Service-Oriented Architecture (SOA)– based architecture framework. The architecture framework is designed to be close to industry standards, especially to the Service Component Architecture (SCA). The framework is language independent and the building blocks of each system, activities and data, are first class citizens. We present a meta model of the architecture framework and discuss its concepts in detail. Through the framework, concepts of an SOA such as wiring, correlation and instantiation can be clarifie