Fluctuations of the front in a one dimensional model of X+Y-->2X

We consider a model of the reaction $X+Y\to 2X$ on the integer lattice in which $Y$ particles do not move while $X$ particles move as independent continuous time, simple symmetric random walks. $Y$ particles are transformed instantaneously to $X$ particles upon contact. We start with a fixed number $a\ge 1$ of $Y$ particles at each site to the right of the origin, and define a class of configurations of the $X$ particles to the left of the origin having a finite $l^1$ norm with a specified exponential weight. Starting from any configuration of $X$ particles to the left of the origin within such a class, we prove a central limit theorem for the position of the rightmost visited site of the $X$ particles

Nafta and industrial efficiency in Baja California

The figures before and after the North America Free Trade Agreement between Canada, Mexico and United States, suggest the intensification of the North region economic dynamics, particularly in the sates of Baja California. This paper attempts to determine whether the state’s extraordinary growth has been led by efficiency improvement or just by factor growth as a consequence of Free Trade and Foreign Direct Investment. The paper finds empirical evidence in both ways.Economic efficiency; productivity; and free trade

One Thousand and One Bubbles

We propose a novel strategy that permits the construction of completely general five-dimensional microstate geometries on a Gibbons-Hawking space. Our scheme is based on two steps. First, we rewrite the bubble equations as a system of linear equations that can be easily solved. Second, we conjecture that the presence or absence of closed timelike curves in the solution can be detected through the evaluation of an algebraic relation. The construction we propose is systematic and covers the whole space of parameters, so it can be applied to find all five-dimensional BPS microstate geometries on a Gibbons-Hawking base. As a first result of this approach, we find that the spectrum of scaling solutions becomes much larger when non-Abelian fields are present. We use our method to describe several smooth horizonless multicenter solutions with the asymptotic charges of three-charge (Abelian and non-Abelian) black holes. In particular, we describe solutions with the centers lying on lines and circles that can be specified with exact precision. We show the power of our method by explicitly constructing a 50-center solution. Moreover, we use it to find the first smooth five-dimensional microstate geometries with arbitrarily small angular momentum.Comment: 33 pages. v2: typos correcte

Economic Growth and Human Development -

This paper explores the links between economic growth and human development, identifying two chains, one from economic growth to human development, and the other, conversely, from human development to economic growth. The various links in each chain are explored, together with a review of some existing empirical material on their importance. The paper examines the significance of the relationships, for the chains as a whole and for particular links in them, with the help of cross-country statistics for the period 1970-92. It finds that there exists a strong positive relationship in both directions and that public expenditure on social services and female education are especially important links determining the strength of the relationship between economic growth and human development, while the investment rate and income distribution are significant links in determining the strength of the relationship between human development and economic growth. The existence of these chains gives rise to the potential for virtuous or vicious cycles of development, with good or bad performance on HD and economic growth reinforcing each other over time. The paper concludes by classifying the actual performance of developing countries into these virtuous and vicious cycles, as well as identifying lop- sided performers, with good performance in one dimension but not the other, and explores how country classification can change over time. We find that lop-sided development almost never persists: countries which are initially lop-sided favoring economic growth always lapse into the vicious category; but countries where HD is favored can move into the virtuous category. This has strong sequencing implications, implying that, while ideally both HD and economic growth should be jointly promoted, HD should be given priority where a choice is necessary.

Transition asymptotics for reaction-diffusion in random media

We describe a universal transition mechanism characterizing the passage to an annealed behavior and to a regime where the fluctuations about this behavior are Gaussian, for the long time asymptotics of the empirical average of the expected value of the number of random walks which branch and annihilate on ${\mathbb Z}^d$, with stationary random rates. The random walks are independent, continuous time rate $2d\kappa$, simple, symmetric, with $\kappa \ge 0$. A random walk at $x\in{\mathbb Z}^d$, binary branches at rate $v_+(x)$, and annihilates at rate $v_-(x)$. The random environment $w$ has coordinates $w(x)=(v_-(x),v_+(x))$ which are i.i.d. We identify a natural way to describe the annealed-Gaussian transition mechanism under mild conditions on the rates. Indeed, we introduce the exponents $F_\theta(t):=\frac{H_1((1+\theta)t)-(1+\theta)H_1(t)}{\theta}$, and assume that $\frac{F_{2\theta}(t)-F_\theta(t)}{\theta\log(\kappa t+e)}\to\infty$ for $|\theta|>0$ small enough, where $H_1(t):=\log$ and $$ denotes the average of the expected value of the number of particles $m(0,t,w)$ at time $t$ and an environment of rates $w$, given that initially there was only one particle at 0. Then the empirical average of $m(x,t,w)$ over a box of side $L(t)$ has different behaviors: if $L(t)\ge e^{\frac{1}{d} F_\epsilon(t)}$ for some $\epsilon >0$ and large enough $t$, a law of large numbers is satisfied; if $L(t)\ge e^{\frac{1}{d} F_\epsilon (2t)}$ for some $\epsilon>0$ and large enough $t$, a CLT is satisfied. These statements are violated if the reversed inequalities are satisfied for some negative $\epsilon$. Applications to potentials with Weibull, Frechet and double exponential tails are given.Comment: To appear in: Probability and Mathematical Physics: A Volume in Honor of Stanislav Molchanov, Editors - AMS | CRM, (2007

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