3,553 research outputs found
Computing topological invariants with one and two-matrix models
A generalization of the Kontsevich Airy-model allows one to compute the
intersection numbers of the moduli space of p-spin curves. These models are
deduced from averages of characteristic polynomials over Gaussian ensembles of
random matrices in an external matrix source. After use of a duality, and of an
appropriate tuning of the source, we obtain in a double scaling limit these
intersection numbers as polynomials in p. One can then take the limit p to -1
which yields a matrix model for orbifold Euler characteristics. The
generalization to a time-dependent matrix model, which is equivalent to a
two-matrix model, may be treated along the same lines ; it also yields a
logarithmic potential with additional vertices for general p.Comment: 30 pages, added references, changed conten
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Modeling Space-Time Data Using Stochastic Differential Equations
This paper demonstrates the use and value of stochastic differential equations for modeling space-time data in two common settings. The first consists of point-referenced or geostatistical data where observations are collected at fixed locations and times. The second considers random point pattern data where the emergence of locations and times is random. For both cases, we employ stochastic differential equations to describe a latent process within a hierarchical model for the data. The intent is to view this latent process mechanistically and endow it with appropriate simple features and interpretable parameters. A motivating problem for the second setting is to model urban development through observed locations and times of new home construction; this gives rise to a space-time point pattern. We show that a spatio-temporal Cox process whose intensity is driven by a stochastic logistic equation is a viable mechanistic model that affords meaningful interpretation for the results of statistical inference. Other applications of stochastic logistic differential equations with space-time varying parameters include modeling population growth and product diffusion, which motivate our first, point-referenced data application. We propose a method to discretize both time and space in order to fit the model. We demonstrate the inference for the geostatistical model through a simulated dataset. Then, we fit the Cox process model to a real dataset taken from the greater Dallas metropolitan area.Business Administratio
Energy radiated from a fluctuating selfdual string
We compute the energy that is radiated from a fluctuating selfdual string in
the large limit of theory using the AdS-CFT correspondence. We
find that the radiated energy is given by a non-local expression integrated
over the string world-sheet. We also make the corresponding computation for a
charged string in six-dimensional classical electrodynamics, thereby
generalizing the Larmor formula for the radiated energy from an accelerated
point particle.Comment: 12 page
Quantum Sturm-Liouville Equation, Quantum Resolvent, Quantum Integrals, and Quantum KdV : the Fast Decrease Case
We construct quantum operators solving the quantum versions of the
Sturm-Liouville equation and the resolvent equation, and show the existence of
conserved currents. The construction depends on the following input data: the
basic quantum field and the regularization .Comment: minor correction
An Effective Field Theory Look at Deep Inelastic Scattering
This talk discusses the effective field theory view of deep inelastic
scattering. In such an approach, the standard factorization formula of a hard
coefficient multiplied by a parton distribution function arises from matching
of QCD onto an effective field theory. The DGLAP equations can then be viewed
as the standard renormalization group equations that determines the cut-off
dependence of the non-local operator whose forward matrix element is the parton
distribution function. As an example, the non-singlet quark splitting functions
is derived directly from the renormalization properties of the non-local
operator itself. This approach, although discussed in the literature, does not
appear to be well known to the larger high energy community. In this talk we
give a pedagogical introduction to this subject.Comment: 11 pages, 1 figure, To appear in Modern Physics Letters
On the algebraic structures connected with the linear Poisson brackets of hydrodynamics type
The generalized form of the Kac formula for Verma modules associated with
linear brackets of hydrodynamics type is proposed. Second cohomology groups of
the generalized Virasoro algebras are calculated. Connection of the central
extensions with the problem of quntization of hydrodynamics brackets is
demonstrated
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