A Model of Two-Dimensional Quantum Gravity in the Strong Coupling Regime

A model of two-dimensional quantum gravity that is the analog of the tensionless string is proposed. The gravitational constant ($k$) is the analog of the Regge slope ($\alpha^{'}$) and it shows that when $k \rightarrow \infty$, $2D$ quantum gravity can be understood as a tensionless string theory embeded in a two-dimensional target space. The temporal coordinate of the target space play the role of time and the wave function can be interpreted as in standard quantum mechanics.Comment: 10pp., Revtex, Si/94/0

Quantum Mechanics on Multiply Connected Manifolds with Applications to One and Two Dimensional Anyons

In these lectures several aspects of anyon in one and two dimensions are considered from the path integral formalism. This paper is based in a set of four lectures given by the author in the "V Latinoamerican Workshop of Particles and Fields, hel in Puebla, Mexico.Comment: 27pp, Late

Static plane symmetric relativistic fluids and empty repelling singular boundaries

We present a detailed analysis of the general exact solution of Einstein's equation corresponding to a static and plane symmetric distribution of matter with density proportional to pressure. We study the geodesics in it and we show that this simple spacetime exhibits very curious properties. In particular, it has a free of matter repelling singular boundary and all geodesics bounce off it.Comment: 9 pages, 1 figure, accepted for publication in Classical and Quantum Gravit

Large Deviations for Random Spectral Measures and Sum Rules

We prove a Large Deviation Principle for the random spec- tral measure associated to the pair $(H_N; e)$ where $H_N$ is sampled in the GUE(N) and e is a fixed unit vector (and more generally in the $\beta$- extension of this model). The rate function consists of two parts. The contribution of the absolutely continuous part of the measure is the reversed Kullback information with respect to the semicircle distribution and the contribution of the singular part is connected to the rate function of the extreme eigenvalue in the GUE. This method is also applied to the Laguerre and Jacobi ensembles, but in thoses cases the expression of the rate function is not so explicit

Conditional Transfers to Promote Local Government Participation in Mexico

Mexico is a very centralized country mainly as a result of the involvement of the federal government (FG) in functions that would be more efficiently provided by subnational governments (SG). The concentration of activities in the FG is the result of two institutional features: the unclear legal assignment of expenditure functions across levels of government, and the assignment of sources of revenue that concentrates a larger share of revenues in hands of the FG. In the presence of multiple uses of federal transfers, and in the absence of information on the costs of providing SG services, the FG has been reasonably reluctant to decentralize more functions. As long as the FG remains in control of most of government revenues, it is important to ensure that the benefits from decentralization also accrue to it. The transfer of functions should avoid SG neglect of those functions that generate benefits to the rest of the country and keep control over the size of transfers. One instrument that can achieve both objectives is a widespread use of conditional grants.

Perfect Numbers in ACL2

A perfect number is a positive integer n such that n equals the sum of all positive integer divisors of n that are less than n. That is, although n is a divisor of n, n is excluded from this sum. Thus 6 = 1 + 2 + 3 is perfect, but 12 < 1 + 2 + 3 + 4 + 6 is not perfect. An ACL2 theory of perfect numbers is developed and used to prove, in ACL2(r), this bit of mathematical folklore: Even if there are infinitely many perfect numbers the series of the reciprocals of all perfect numbers converges.Comment: In Proceedings ACL2 2015, arXiv:1509.0552

Equivalence of the Traditional and Non-Standard Definitions of Concepts from Real Analysis

ACL2(r) is a variant of ACL2 that supports the irrational real and complex numbers. Its logical foundation is based on internal set theory (IST), an axiomatic formalization of non-standard analysis (NSA). Familiar ideas from analysis, such as continuity, differentiability, and integrability, are defined quite differently in NSA-some would argue the NSA definitions are more intuitive. In previous work, we have adopted the NSA definitions in ACL2(r), and simply taken as granted that these are equivalent to the traditional analysis notions, e.g., to the familiar epsilon-delta definitions. However, we argue in this paper that there are circumstances when the more traditional definitions are advantageous in the setting of ACL2(r), precisely because the traditional notions are classical, so they are unencumbered by IST limitations on inference rules such as induction or the use of pseudo-lambda terms in functional instantiation. To address this concern, we describe a formal proof in ACL2(r) of the equivalence of the traditional and non-standards definitions of these notions.Comment: In Proceedings ACL2 2014, arXiv:1406.123