Bad configurations for random walk in random scenery and related subshifts

Article / Letter to editorMathematisch Instituu

Bad configurations for random walk in random scenery and related subshifts

In this paper we consider an arbitrary irreducible random walk on , d1, with i.i.d. increments, together with an arbitrary i.i.d. random scenery. Walk and scenery are assumed to be independent. Random walk in random scenery (RWRS) is the random process where time is indexed by , and at each unit of time both the step taken by the walk and the scenery value at the site that is visited are registered. Bad configurations for RWRS are the discontinuity points of the conditional probability distribution for the configuration at the origin of time given the configuration at all other times. We show that the set of bad configurations is non-empty. We give a complete description of this set and compute its probability under the random scenery measure. Depending on the type of random walk, this probability may be zero or positive. For simple symmetric random walk we get three different types of behavior depending on whether d=1,2, d=3,4 or d5. Our classification is actually valid for a class of subshifts having a certain determinative property, which we call specifiable, of which RWRS is an example. We also consider bad configurations w.r.t. a finite time interval (replacing the origin) and obtain an almost complete generalization of our results. Remarkably, this extension turns out to be somewhat delicate

Comparing methods to approach cumulative effects in the North-East Atlantic: CUMULEO case study

OSPAR Intersessional Correspondence Group – Cumulative Effects (ICG-C), part of OSPAR commission Environmental Impact of Human Activities (EIHA), is seeking for common approaches on (cross-border) cumulative effects. At the OSPAR ICG-C meeting of 12-13 December 2012 (Copenhagen), three cumulative effects assessment (CEA) methods have been discussed: CUMULEO; ODEMM; and HARMONY. It was concluded that a case study could help in finding best available approaches and tools within the three methods for a specific question. This report describes the case study based on the CUMULEO method

Bad configurations for random walk in random scenery and related subshifts

Analysis and Stochastic

Quickscan potentiële natuurwaarden in bestaande Nederlandse offshorewindparken

In het kader van het Nationaal Waterplan worden mogelijkheden verkend om offshorewindparken open te stellen voor doorvaart en medegebruik. In dit rapport wordt op basis van literatuuronderzoek een overzicht gegeven van (potentiële) natuurwaarden voor drie bestaande windparken, OWEZ (Offshore Windpark Egmond aan Zee), PAWP (Prinses Amalia Windpark) en Luchterduinen. Het gaat hierbij om biogene riffen (bestaand of potentieel), hardsubstraatgemeenschappen (bestaand of potentieel), vissoorten (rodelijstsoorten), zeezoogdieren en vogels en overige beleidsrelevante soorten (vleermuizen). Vervolgens wordt een beperkt aantal potentiële activiteiten beschreven (handlijnvisserij, visserij met korven, oesterkweek met manden, staand want, mosselteelt) en wordt verkend welke mogelijke invloed deze activiteiten hebben op de (potentiële) natuurwaarden, waarbij de nadruk ligt op beleidsrelevante soorten in het kader van Natura 2000 (Habitatrichtlijn) en de Kaderrichtlijn Mariene Strategie (KRM)

Josephson Persistent-Current Qubit

A qubit was designed that can be fabricated with conventional electron beam lithography and is suited for integration into a large quantum computer. The qubit consists of a micrometer-sized loop with three or four Josephson junctions; the two qubit states have persistent currents of opposite direction. Quantum superpositions of these states are obtained by pulsed microwave modulation of the enclosed magnetic flux by currents in control lines. A superconducting flux transporter allows for controlled transfer between qubits of the flux that is generated by the persistent currents, leading to entanglement of qubit information