76 research outputs found
Bulk Universality and Related Properties of Hermitian Matrix Models
We give a new proof of universality properties in the bulk of spectrum of the
hermitian matrix models, assuming that the potential that determines the model
is globally and locally function (see Theorem \ref{t:U.t1}).
The proof as our previous proof in \cite{Pa-Sh:97} is based on the orthogonal
polynomial techniques but does not use asymptotics of orthogonal polynomials.
Rather, we obtain the -kernel as a unique solution of a certain non-linear
integro-differential equation that follows from the determinant formulas for
the correlation functions of the model. We also give a simplified and
strengthened version of paper \cite{BPS:95} on the existence and properties of
the limiting Normalized Counting Measure of eigenvalues. We use these results
in the proof of universality and we believe that they are of independent
interest
Tall tales from de Sitter space II: Field theory dualities
We consider the evolution of massive scalar fields in (asymptotically) de
Sitter spacetimes of arbitrary dimension. Through the proposed dS/CFT
correspondence, our analysis points to the existence of new nonlocal dualities
for the Euclidean conformal field theory. A massless conformally coupled scalar
field provides an example where the analysis is easily explicitly extended to
'tall' background spacetimes.Comment: 31 pages, 2 figure
Level-Spacing Distributions and the Bessel Kernel
The level spacing distributions which arise when one rescales the Laguerre or
Jacobi ensembles of hermitian matrices is studied. These distributions are
expressible in terms of a Fredholm determinant of an integral operator whose
kernel is expressible in terms of Bessel functions of order . We derive
a system of partial differential equations associated with the logarithmic
derivative of this Fredholm determinant when the underlying domain is a union
of intervals. In the case of a single interval this Fredholm determinant is a
Painleve tau function.Comment: 18 pages, resubmitted to make postscript compatible, no changes to
manuscript conten
Optimal estimation of qubit states with continuous time measurements
We propose an adaptive, two steps strategy, for the estimation of mixed qubit
states. We show that the strategy is optimal in a local minimax sense for the
trace norm distance as well as other locally quadratic figures of merit. Local
minimax optimality means that given identical qubits, there exists no
estimator which can perform better than the proposed estimator on a
neighborhood of size of an arbitrary state. In particular, it is
asymptotically Bayesian optimal for a large class of prior distributions.
We present a physical implementation of the optimal estimation strategy based
on continuous time measurements in a field that couples with the qubits.
The crucial ingredient of the result is the concept of local asymptotic
normality (or LAN) for qubits. This means that, for large , the statistical
model described by identically prepared qubits is locally equivalent to a
model with only a classical Gaussian distribution and a Gaussian state of a
quantum harmonic oscillator.
The term `local' refers to a shrinking neighborhood around a fixed state
. An essential result is that the neighborhood radius can be chosen
arbitrarily close to . This allows us to use a two steps procedure by
which we first localize the state within a smaller neighborhood of radius
, and then use LAN to perform optimal estimation.Comment: 32 pages, 3 figures, to appear in Commun. Math. Phy
Effective Action for the Quark-Meson Model
The scale dependence of an effective average action for mesons and quarks is
described by a nonperturbative flow equation. The running couplings lead to
spontaneous chiral symmetry breaking. We argue that for strong Yukawa coupling
between quarks and mesons the low momentum physics is essentially determined by
infrared fixed points. This allows us to establish relations between various
parameters related to the meson potential. The results for and
\VEV{\olpsi\psi} are not very sensitive to the poorly known details of the
quark--meson effective action at scales where the mesonic bound states form.
For realistic constituent quark masses we find around 100\MeV.Comment: 56 pages (including 10 figures and 1 table), uses epsf.st
Crises and collective socio-economic phenomena: simple models and challenges
Financial and economic history is strewn with bubbles and crashes, booms and
busts, crises and upheavals of all sorts. Understanding the origin of these
events is arguably one of the most important problems in economic theory. In
this paper, we review recent efforts to include heterogeneities and
interactions in models of decision. We argue that the Random Field Ising model
(RFIM) indeed provides a unifying framework to account for many collective
socio-economic phenomena that lead to sudden ruptures and crises. We discuss
different models that can capture potentially destabilising self-referential
feedback loops, induced either by herding, i.e. reference to peers, or
trending, i.e. reference to the past, and account for some of the phenomenology
missing in the standard models. We discuss some empirically testable
predictions of these models, for example robust signatures of RFIM-like herding
effects, or the logarithmic decay of spatial correlations of voting patterns.
One of the most striking result, inspired by statistical physics methods, is
that Adam Smith's invisible hand can badly fail at solving simple coordination
problems. We also insist on the issue of time-scales, that can be extremely
long in some cases, and prevent socially optimal equilibria to be reached. As a
theoretical challenge, the study of so-called "detailed-balance" violating
decision rules is needed to decide whether conclusions based on current models
(that all assume detailed-balance) are indeed robust and generic.Comment: Review paper accepted for a special issue of J Stat Phys; several
minor improvements along reviewers' comment
Diagnostic value of computed tomography, radiography and ultrasonography in metacarpophalangeal joint disorders in horses
Chirality and Symmetry Breaking in a discrete internal Space
In previous papers the permutation group S_4 has been suggested as an
ordering scheme for elementary particles, and the appearance of this finite
symmetry group was taken as indication for the existence of a discrete inner
symmetry space underlying elementary particle interactions. Here it is pointed
out that a more suitable choice than the tetrahedral group S_4 is the
pyritohedral group A_4 x Z_2 because its vibrational spectrum exhibits exactly
the mass multiplet structure of the 3 fermion generations. Furthermore it is
noted that the same structure can also be obtained from a primordial symmetry
breaking S_4 --> A_4. Since A_4 is a chiral group, while S_4 is achiral, an
argument can be given why the chirality of the inner pyritohedral symmetry
leads to parity violation of the weak interactions.Comment: 42 pages, 3 table
Fratura de fĂbula e lesĂ”es de ligamento colateral e menisco lateral em muar: relato de caso
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