1,680 research outputs found

### On the Stability of the Quenched State in Mean Field Spin Glass Models

While the Gibbs states of spin glass models have been noted to have an
erratic dependence on temperature, one may expect the mean over the disorder to
produce a continuously varying ``quenched state''. The assumption of such
continuity in temperature implies that in the infinite volume limit the state
is stable under a class of deformations of the Gibbs measure. The condition is
satisfied by the Parisi Ansatz, along with an even broader stationarity
property. The stability conditions have equivalent expressions as marginal
additivity of the quenched free energy. Implications of the continuity
assumption include constraints on the overlap distribution, which are expressed
as the vanishing of the expectation value for an infinite collection of
multi-overlap polynomials. The polynomials can be computed with the aid of a
"real"-replica calculation in which the number of replicas is taken to zero.Comment: 17 pages, LaTex, Revised June 5, 199

### Fractional Moment Estimates for Random Unitary Operators

We consider unitary analogs of $d-$dimensional Anderson models on $l^2(\Z^d)$
defined by the product $U_\omega=D_\omega S$ where $S$ is a deterministic
unitary and $D_\omega$ is a diagonal matrix of i.i.d. random phases. The
operator $S$ is an absolutely continuous band matrix which depends on
parameters controlling the size of its off-diagonal elements. We adapt the
method of Aizenman-Molchanov to get exponential estimates on fractional moments
of the matrix elements of $U_\omega(U_\omega -z)^{-1}$, provided the
distribution of phases is absolutely continuous and the parameters correspond
to small off-diagonal elements of $S$. Such estimates imply almost sure
localization for $U_\omega$

### Constructive Fractional-Moment Criteria for Localization in Random Operators

We present a family of finite-volume criteria which cover the regime of
exponential decay for the fractional moments of Green functions of operators
with random potentials. Such decay is a technically convenient characterization
of localization for it is known to imply spectral localization, absence of
level repulsion, dynamical localization and a related condition which plays a
significant role in the quantization of the Hall conductance in two-dimensional
Fermi gases. The constructive criteria also preclude fast power-law decay of
the Green functions at mobility edges.Comment: Announcement and summary of results whose proofs are given elsewhere.
LaTex (10 pages), uses Elsevier "elsart" files (attached

### Localization Bounds for Multiparticle Systems

We consider the spectral and dynamical properties of quantum systems of $n$
particles on the lattice $\Z^d$, of arbitrary dimension, with a Hamiltonian
which in addition to the kinetic term includes a random potential with iid
values at the lattice sites and a finite-range interaction. Two basic
parameters of the model are the strength of the disorder and the strength of
the interparticle interaction. It is established here that for all $n$ there
are regimes of high disorder, and/or weak enough interactions, for which the
system exhibits spectral and dynamical localization. The localization is
expressed through bounds on the transition amplitudes, which are uniform in
time and decay exponentially in the Hausdorff distance in the configuration
space. The results are derived through the analysis of fractional moments of
the $n$-particle Green function, and related bounds on the eigenfunction
correlators

### Institutional Efficiency, Monitoring Costs, and the Investment Share of FDI

This paper models and tests the implications of costly enforcement of property rights on the pattern of foreign direct investment (FDI). We posit that domestic agents have a comparative advantage over foreign agents in overcoming some of the obstacles associated with corruption and weak institutions. We model these circumstances in a principal-agent framework with costly ex-post monitoring and enforcement of an ex-ante labor contract. Ex-post monitoring and enforcement costs are assumed to be lower for domestic entrepreneurs than for foreign ones, but foreign producers enjoy a countervailing productivity advantage. Under these asymmetries, multinationals pay higher wages than domestic producers, in line with the insight of efficiency wages and with the evidence about the multinationals wage premium.' FDI is also more sensitive to increases in enforcement costs. We then test this prediction for a cross section of developing countries. We use Mauro's (2001) index of economic corruption as an indicator of the strength of property right enforcement within a given country. We compare corruption levels for a large cross section of countries in 1989 to subsequent FDI flows from 1990 to 1999. We find that corruption is negatively associated with the ratio of subsequent foreign direct investment flows to both gross fixed capital formation and to private investment. This finding is true for both simple cross-sections and for cross-sections weighted by country size.

### Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method

A technically convenient signature of Anderson localization is exponential
decay of the fractional moments of the Green function within appropriate energy
ranges. We consider a random Hamiltonian on a lattice whose randomness is
generated by the sign-indefinite single-site potential, which is however
sign-definite at the boundary of its support. For this class of Anderson
operators we establish a finite-volume criterion which implies that above
mentioned the fractional moment decay property holds. This constructive
criterion is satisfied at typical perturbative regimes, e. g. at spectral
boundaries which satisfy 'Lifshitz tail estimates' on the density of states and
for sufficiently strong disorder. We also show how the fractional moment method
facilitates the proof of exponential (spectral) localization for such random
potentials.Comment: 29 pages, 1 figure, to appear in AH

### Exponential dynamical localization for the almost Mathieu operator

We prove that the exponential moments of the position operator stay bounded
for the supercritical almost Mathieu operator with Diophantine frequency

### Decay Properties of the Connectivity for Mixed Long Range Percolation Models on $\Z^d$

In this short note we consider mixed short-long range independent bond
percolation models on $\Z^{k+d}$. Let $p_{uv}$ be the probability that the edge
$(u,v)$ will be open. Allowing a $x,y$-dependent length scale and using a
multi-scale analysis due to Aizenman and Newman, we show that the long distance
behavior of the connectivity $\tau_{xy}$ is governed by the probability
$p_{xy}$. The result holds up to the critical point.Comment: 6 page

### Localization criteria for Anderson models on locally finite graphs

We prove spectral and dynamical localization for Anderson models on locally
finite graphs using the fractional moment method. Our theorems extend earlier
results on localization for the Anderson model on \ZZ^d. We establish
geometric assumptions for the underlying graph such that localization can be
proven in the case of sufficiently large disorder

### Sargent-Wallace Meets Krugman-Flood-Garber, or: Why Sovereign Debt Swaps Don't Avert Macroeconomic Crises

This paper argues that the frequent failure of the debt swaps is not an accident. Instead, it follows from fundamental forces driven by the market's assessment of the scarcity of fiscal revenue relative to the demand for fiscal outlays. It follows from the observation that arbitrage forces systematically impact prices in asset markets. Ignoring these price adjustments would lead to too optimistic an assessment of the gains from swaps or buybacks. A by-product of our paper is to highlight the perils of financial engineering that ignores the intertemporal constraints imposed by fiscal fundamentals. As a country approaches the range of partial default (either on domestic or external debt), swaps may not provide the expected breathing room and could even bring the crisis forward. Our methodology combines three independent themes: exchange rate crises as the manifestation of excessive monetary injections [Krugman-Flood-Garber], the fiscal theory of inflation [Sargent-Wallace (1981)], and sovereign debt. The integrated framework derives devaluation and external debt repudiation as part of a public-finance optimizing problem. We shows that under conditions similar to those which prevailed in Russia and Argentina prior to their meltdown, swaps are not just neutral, but could actually make the situation worse and even trigger a speculative attack. An unsettlingly clear implication of the model is that there may be very few options left once public debt reaches levels regarded as unsustainable in relation to fiscal fundamentals. Dollarization only makes matters worse, and pushes the debt write-down option to the fore.

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