Pairings of automorphic distributions

We present a pairing of automorphic distributions that applies in situations where a Lie group acts with an open orbit on a product of generalized flag varieties. The pairing gives meaning to an integral of products of automorphic distributions on these varieties. This generalizes classical integral representations or "Rankin-Selberg integrals" of L-functions, and gives new constructions and analytic continuations of automorphic L-functions. Keywords: Automorphic forms, invariant pairings, automorphic distributions, L-functions, analytic continuation, rapid decay.Comment: 19 pages, to appear in Mathematische Annale

Grafted Rods: A Tilting Phase Transition

A tilting phase transition is predicted for systems comprising rod like molecules which are irreversibly grafted to a flat surface, so that the non interacting rods are perpendicularly oriented. The transition is controlled by the grafting density $\rho$. It occurs as $\rho$ increases as a result of the interplay between two energies. Tilt is favoured by the van-der-Waals attraction between the rods. It is opposed by the bending elasticity of the grafting functionality. The role of temperature is discussed, and the tilting mechanism is compared to other tilting transitions reported in the literature.Comment: 21 pages, 2 figures, to appear in Journal de Physique I

The Dirac propagator in the extreme Kerr metric

Starting with the Dirac equation in the extreme Kerr metric we derive an integral representation for the propagator of solutions of the Cauchy problem with initial data in the class of smooth compactly supported functions.Comment: 9 pages, one more reference adde

The Highly Oscillatory Behavior of Automorphic Distributions for SL(2)

Automorphic distributions for SL(2) arise as boundary values of modular forms and, in a more subtle manner, from Maass forms. In the case of modular forms of weight one or of Maass forms, the automorphic distributions have continuous first antiderivatives. We recall earlier results of one of us on the Holder continuity of these continuous functions and relate them to results of other authors; this involves a generalization of classical theorems on Fourier series by S. Bernstein and Hardy-Littlewood. We then show that the antiderivatives are non-differentiable at all irrational points, as well as all, or in certain cases, some rational points. We include graphs of several of these functions, which clearly display a high degree of oscillation. Our investigations are motivated in part by properties of "Riemann's nondifferentiable function", also known as "Weierstrass' function".Comment: 27 pages, 6 Figures; version 2 corrects misprints and updates reference

The Camp View of Inflation Forecasts

Analyzing sample moments of survey forecasts, we derive disagreement and un- certainty measures for the short- and medium term inflation outlook. The latter provide insights into the development of inflation forecast uncertainty in the context of a changing macroeconomic environment since the beginning of 2008. Motivated by the debate on the role of monetary aggregates and cyclical variables describing a Phillips-curve logic, we develop a macroeconomic indicator spread which is assumed to drive forecasters’ judgments. Empirical evidence suggests procyclical dynamics between disagreement among forecasters, individual forecast uncertainty and the macro-spread. We call this approach the camp view of inflation forecasts and show that camps form up whenever the spread widens.monetary policy, survey forecasts, inflation uncertainty, heterogenous beliefs and expectations, monetary aggregates

Medium-run macrodynamics and the consensus view of stabilization policy

Policy implications of the present consensus view of stabilization policy depend on specific assumptions with regard to the equilibrium level of production. Thereby, the interpretation of equilibrium output rests on a separation of supply-side and demandside adjustment to macroeconomic shocks promoting a dichotomy of short-term and long-term macrodynamics. In contrast to this, there are several channels that promote procyclical stimulus of aggregate demand and a changing factor utilization to the accumulation and efficiency of an economy’s productive capacity. Medium-run macrodynamics call for a rather endogenous explanation of production capacity and challenge the uniqueness of long-term equilibria.Monetary policy, medium-run macrodynamics, long-term nonneutrality, capacity utilization.

Monte Carlo simulations of liquid crystals near rough walls

The effect of surface roughness on the structure of liquid crystalline fluids near solid substrates is studied by Monte Carlo simulations. The liquid crystal is modeled as a fluid of soft ellipsoidal molecules and the substrate is modeled as a hard wall that excludes the centers of mass of the fluid molecules. Surface roughness is introduced by embedding a number of molecules with random positions and orientations within the wall. It is found that the density and order near the wall are reduced as the wall becomes rougher, i.e., the number of embedded molecules is increased). Anchoring coefficients are determined from fluctuations in the reciprocal space order tensor. It is found that the anchoring strength decreases with increasing surface roughness