1,554 research outputs found
Reserve Requirements on Sovereign Debt in the Presence of Moral Hazard -- on Debtors or Creditors?
This paper characterizes the effects of reserve requirements on financial loans in the presence of moral hazard on the lender side (i.e., the anticipation that the taxpayer will bailout lending banks if large default will occur) and sovereign risk on the borrower side. The impacts of such reserve requirements on the equilibrium degree of default risk and borrowing are analyzed, and their welfare implications for both the borrowing and the lending nations discussed. More generous bailouts financed by the high income block encourage borrowing and increase the probability of default. We show that the introduction of a reserve requirement in either country reduces the risk of default and raises the welfare of both the high income block and the emerging market economies. In these circumstances, the lender's optimal reserve requirement is shown to increase with the expected bailout. Such a policy induces the lender to internalize the expected tax payer cost of the bailout. Thus a more generous bailout that is accompanied by an optimal adjustment in the lender's reserve requirements exactly neutralizes its effects on welfare, leaving welfare in both countries unchanged. Unlike the case of the lender, the effect of the more generous bailout on the borrower's optimal reserve requirement is ambiguous. The imposition of the reserve requirement may also improve the availability of information about the debt exposure of the emerging market economies, which by itself will reduce the optimal lender's reserve requirements, and may prevent drying up' the market for sovereign debt.
Localization Bounds for Multiparticle Systems
We consider the spectral and dynamical properties of quantum systems of
particles on the lattice , 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 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 -particle Green function, and related bounds on the eigenfunction
correlators
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
Multi-Particle Anderson Localisation: Induction on the Number of Particles
This paper is a follow-up of our recent papers \cite{CS08} and \cite{CS09}
covering the two-particle Anderson model. Here we establish the phenomenon of
Anderson localisation for a quantum -particle system on a lattice
with short-range interaction and in presence of an IID external potential with
sufficiently regular marginal cumulative distribution function (CDF). Our main
method is an adaptation of the multi-scale analysis (MSA; cf. \cite{FS},
\cite{FMSS}, \cite{DK}) to multi-particle systems, in combination with an
induction on the number of particles, as was proposed in our earlier manuscript
\cite{CS07}. Similar results have been recently obtained in an independent work
by Aizenman and Warzel \cite{AW08}: they proposed an extension of the
Fractional-Moment Method (FMM) developed earlier for single-particle models in
\cite{AM93} and \cite{ASFH01} (see also references therein) which is also
combined with an induction on the number of particles.
An important role in our proof is played by a variant of Stollmann's
eigenvalue concentration bound (cf. \cite{St00}). This result, as was proved
earlier in \cite{C08}, admits a straightforward extension covering the case of
multi-particle systems with correlated external random potentials: a subject of
our future work. We also stress that the scheme of our proof is \textit{not}
specific to lattice systems, since our main method, the MSA, admits a
continuous version. A proof of multi-particle Anderson localization in
continuous interacting systems with various types of external random potentials
will be published in a separate papers
The Number of Incipient Spanning Clusters in Two-Dimensional Percolation
Using methods of conformal field theory, we conjecture an exact form for the
probability that n distinct clusters span a large rectangle or open cylinder of
aspect ratio k, in the limit when k is large.Comment: 9 pages, LaTeX, 1 eps figure. Additional references and comparison
with existing numerical results include
The Anderson Model as a Matrix Model
In this paper we describe a strategy to study the Anderson model of an
electron in a random potential at weak coupling by a renormalization group
analysis. There is an interesting technical analogy between this problem and
the theory of random matrices. In d=2 the random matrices which appear are
approximately of the free type well known to physicists and mathematicians, and
their asymptotic eigenvalue distribution is therefore simply Wigner's law.
However in d=3 the natural random matrices that appear have non-trivial
constraints of a geometrical origin. It would be interesting to develop a
general theory of these constrained random matrices, which presumably play an
interesting role for many non-integrable problems related to diffusion. We
present a first step in this direction, namely a rigorous bound on the tail of
the eigenvalue distribution of such objects based on large deviation and
graphical estimates. This bound allows to prove regularity and decay properties
of the averaged Green's functions and the density of states for a three
dimensional model with a thin conducting band and an energy close to the border
of the band, for sufficiently small coupling constant.Comment: 23 pages, LateX, ps file available at
http://cpth.polytechnique.fr/cpth/rivass/articles.htm
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
Infrared bound and mean-field behaviour in the quantum Ising model
We prove an infrared bound for the transverse field Ising model. This bound
is stronger than the previously known infrared bound for the model, and allows
us to investigate mean-field behaviour. As an application we show that the
critical exponent for the susceptibility attains its mean-field value
in dimension at least 4 (positive temperature), respectively 3
(ground state), with logarithmic corrections in the boundary cases.Comment: 42 pages, 5 figures, to appear in CM
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
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