698 research outputs found
The Exact Renormalization Group
This is a very brief introduction to Wilson's Renormalization Group with
emphasis on mathematical developments.Comment: 17 pages, AMS LaTeX. Contribution to the Encyclopedia of Mathematical
Physics (Elsevier, 2006). Typos, journal reference correcte
Renormalization group approach to interacting polymerised manifolds
We propose to study the infrared behaviour of polymerised (or tethered)
random manifolds of dimension D interacting via an exclusion condition with a
fixed impurity in d-dimensional Euclidean space in which the manifold is
embedded. We prove rigorously, via methods of Wilson's renormalization group,
the convergence to a non Gaussian fixed point for suitably chosen physical
parameters.Comment: 90 pages, Plain tex file. Updated version with more detailed
introduction and added reference
Finite range Decomposition of Gaussian Processes
Let \D be the finite difference Laplacian associated to the lattice
\bZ^{d}. For dimension , and a sufficiently large
positive dyadic integer, we prove that the integral kernel of the resolvent
G^{a}:=(a-\D)^{-1} can be decomposed as an infinite sum of positive
semi-definite functions of finite range, for
. Equivalently, the Gaussian process on the lattice with
covariance admits a decomposition into independent Gaussian processes
with finite range covariances. For , has a limiting scaling form
as .
As a corollary, such decompositions also exist for fractional powers
(-\D)^{-\alpha/2}, . The results of this paper give an
alternative to the block spin renormalization group on the lattice.Comment: 26 pages, LaTeX, paper in honour of G.Jona-Lasinio.Typos corrected,
corrections in section 5 and appendix
Labor Productivity in Austria Between 1964 and 1980
Input-output analysis has found widespread empirical application, in studies of how certain industrial sectors react to changes in national and international economic conditions and in static and dynamic investigations of the interrelationships between industries. Since 1979 IIASA has been consistently active in this field, primarily through extensive collaboration with the Inter-Industry Forecasting Program (INFORUM) coordinated at the University of Maryland by Clopper Almon and Douglas Nyhus. IIASA's new aims have been to further the development of econometric input-output models, to assist in the linkage of national models, and to participate in and extend the international network of collaborating scientists.
To date, eighteen national models have been installed at IIASA, the software package SLIMFORP has been distributed widely, and linked runs of some of the national models have been carried out. Furthermore, annual task force meetings on input-output modeling have served to bring together present and prospective members of the INFORUM-IIASA "family" to review progress and to exchange ideas for further work.
In this paper Peter Mitter (Institute for Advanced Studies, Vienna) and Jiri Skolka (Austrian Institute for Economic Research, Vienna, and also a participant in several recent task force and advisory meetings at IIASA) present the results of an analysis of labor productivity in Austria between 1964 and 1980. The study was carried out as part of continuing work on an Austrian dynamic input-output model within the INFORUM framework, and the results will form the basis for the determination of the model's productivity functions
CRITICAL (Phi^{4}_{3,\epsilon})
The Euclidean (\phi^{4})_{3,\epsilon model in corresponds to a
perturbation by a interaction of a Gaussian measure on scalar fields
with a covariance depending on a real parameter in the range . For one recovers the covariance of a massless
scalar field in . For is a marginal interaction.
For the covariance continues to be Osterwalder-Schrader and
pointwise positive. After introducing cutoffs we prove that for ,
sufficiently small, there exists a non-gaussian fixed point (with one unstable
direction) of the Renormalization Group iterations. These iterations converge
to the fixed point on its stable (critical) manifold which is constructed.Comment: 49 pages, plain tex, macros include
On the Convergence to the Continuum of Finite Range Lattice Covariances
In J. Stat. Phys. 115, 415-449 (2004) Brydges, Guadagni and Mitter proved the
existence of multiscale expansions of a class of lattice Green's functions as
sums of positive definite finite range functions (called fluctuation
covariances). The lattice Green's functions in the class considered are
integral kernels of inverses of second order positive self adjoint operators
with constant coefficients and fractional powers thereof. The fluctuation
coefficients satisfy uniform bounds and the sequence converges in appropriate
norms to a smooth, positive definite, finite range continuum function. In this
note we prove that the convergence is actually exponentially fast.Comment: 14 pages. We have added further references as well as a proof of
Corollary 2.2. This version submitted for publicatio
On an Information and Control Architecture for Future Electric Energy Systems
This paper presents considerations towards an information and control
architecture for future electric energy systems driven by massive changes
resulting from the societal goals of decarbonization and electrification. This
paper describes the new requirements and challenges of an extended information
and control architecture that need to be addressed for continued reliable
delivery of electricity. It identifies several new actionable information and
control loops, along with their spatial and temporal scales of operation, which
can together meet the needs of future grids and enable deep decarbonization of
the electricity sector. The present architecture of electric power grids
designed in a different era is thereby extensible to allow the incorporation of
increased renewables and other emerging electric loads.Comment: This paper is accepted, to appear in the Proceedings of the IEE
Completeness of Wilson loop functionals on the moduli space of and -connections
The structure of the moduli spaces \M := \A/\G of (all, not just flat)
and connections on a n-manifold is analysed. For any
topology on the corresponding spaces \A of all connections which satisfies
the weak requirement of compatibility with the affine structure of \A, the
moduli space \M is shown to be non-Hausdorff. It is then shown that the
Wilson loop functionals --i.e., the traces of holonomies of connections around
closed loops-- are complete in the sense that they suffice to separate all
separable points of \M. The methods are general enough to allow the
underlying n-manifold to be topologically non-trivial and for connections to be
defined on non-trivial bundles. The results have implications for canonical
quantum general relativity in 4 and 3 dimensions.Comment: Plain TeX, 7 pages, SU-GP-93/4-
Renormalization of the Hamiltonian and a geometric interpretation of asymptotic freedom
Using a novel approach to renormalization in the Hamiltonian formalism, we
study the connection between asymptotic freedom and the renormalization group
flow of the configuration space metric. It is argued that in asymptotically
free theories the effective distance between configuration decreases as high
momentum modes are integrated out.Comment: 22 pages, LaTeX, no figures; final version accepted in Phys.Rev.D;
added reference and appendix with comment on solution of eq. (9) in the tex
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