Aid and development : issues and reflections

The paper has three main sections. The first is a review of two particular propositions which appear in Dambisa Moyo’s 2009 book Dead Aid which were not subjected to rigorous analysis in the reviews which appeared following its publication. The finding is that neither proposition survives serious scrutiny – that aid is responsible for most of sub-Saharan Africa’s economic woes and that the international bond market represents a viable alternative to foreign aid for the finance of development-oriented investment. The second questions some of the characteristics and uses of the World Bank’s Country Policy and Institutional Assessment (CPIA), particularly focussing on the use of an essentially ordinal measure in cardinal applications. The third subjects the UK Department for International Development’s Needs-Effectiveness Index to critical review, concluding that further consideration of its attributes is necessary

Historical Schools of Economics: German and English

This paper contrasts the German and English traditions of "Historical Economics" and explains their differences by positioning these two traditions in the specific institutional contexts in which they developed.Historical Economics, Historical School, Neoclassicism, German Economics

On the large time asymptotics of decaying Burgers turbulence

The decay of Burgers turbulence with compactly supported Gaussian "white noise" initial conditions is studied in the limit of vanishing viscosity and large time. Probability distribution functions and moments for both velocities and velocity differences are computed exactly, together with the "time-like" structure functions . The analysis of the answers reveals both well known features of Burgers turbulence, such as the presence of dissipative anomaly, the extreme anomalous scaling of the velocity structure functions and self similarity of the statistics of the velocity field, and new features such as the extreme anomalous scaling of the "time-like" structure functions and the non-existence of a global inertial scale due to multiscaling of the Burgers velocity field. We also observe that all the results can be recovered using the one point probability distribution function of the shock strength and discuss the implications of this fact for Burgers turbulence in general.Comment: LATEX, 25 pages, The present paper is an extension of the talk delivered at the workshop on intermittency in turbulent systems, Newton Institute, Cambridge, UK, June 199

Hitting properties of a random string

We consider Funaki's model of a random string taking values in R^d. It is specified by the following stochastic PDE, du = u_{xx} + W, where W=W(x,t) is two-parameter white noise, also taking values in R^d. We study hitting properties, double points, and recurrence. The main difficulty is that the process has the Markov property in time, but not in space. We find: (1) The string hits points if d<6. (2) For fixed t, there are points x,y such that u(t,x)=u(t,y) iff d < 4. (3) There exist points t,x,y such that u(t,x)=u(t,y) iff d < 8. (4) There exist points s,t,x,y such that u(t,x)=u(s,y) iff d < 12. (5) The string is recurrent iff d < 7

Pfaffian formulae for one dimensional coalescing and annihilating systems

The paper considers instantly coalescing, or instantly annihilating, systems of one-dimensional Brownian particles on the real line. Under maximal entrance laws, the distribution of the particles at a fixed time is shown to be Pfaffian point processes closely related to the Pfaffian point process describing one dimensional distribution of real eigenvalues in the real Ginibre ensemble of random matrices. As an application, an exact large time asymptotic for the n-point density function for coalescing particles is derived

Multi-point correlations for two dimensional coalescing random walks

This paper considers an infinite system of instantaneously coalescing rate one simple random walks on $\mathbb{Z}^2$, started from the initial condition with all sites in $\mathbb{Z}^2$ occupied. We show that the correlation functions of the model decay, for any $N \geq 2$, as $$\rho_N (x_1,\ldots,x_N;t) = \frac{c_0(x_1,\ldots,x_N)}{\pi^N} (\log t)^{N-{N \choose 2}} t^{-N} \left(1 + O\left( \frac{1}{\log^{\frac12-\delta}\!t} \right) \right)$$ as $t \to\infty$. This generalises the results for $N=1$ due to Bramson and Griffeath and confirms a prediction in the physics literature for $N>1$. An analogous statement holds for instantaneously annihilating random walks. The key tools are the known asymptotic $\rho_1(t) \sim \log t/\pi t$ due to Bramson and Griffeath, and the non-collision probability $p_{NC}(t)$, that no pair of a finite collection of $N$ two dimensional simple random walks meets by time $t$, whose asymptotic $p_{NC}(t) \sim c_0 (\log t)^{-{N \choose 2}}$ was found by Cox, Merle and Perkins. This paper re-derives the asymptotics both for $\rho_1(t)$ and $p_{NC}(t)$ by proving that these quantities satisfy {\it effective rate equations}, that is approximate differential equations at large times. This approach can be regarded as a generalisation of the Smoluchowski theory of renormalised rate equations to multi-point statistics.Comment: 26 page

One dimensional annihilating particle systems as extended Pfaffian point processes

We prove that the multi-time particle distributions for annihilating Brownian motions, under the maximal entrance law on the real line, are extended Pfaffian point processesComment: An earlier version of this paper falsely stated that the multi-time distributions of coalescing Brownian motions (CBM's) were also an extended Pfaffian point process. This erroneous claim has been removed from the current version. We do not have a simple description of the multi-time distributions for CBM