1,045 research outputs found
On the Spectral properties of Multi-branes, M2 and M5 branes
In this note we summarize some of the properties found in several papers. We
characterize spectral properties of the quantum mechanical hamiltonian of
theories with fermionic degrees of freedom beyond semiclassical approximation.
We obtain a general class of bosonic polynomial potentials for which the
Schr\"oedinger operator has a discrete spectrum. This class includes all the
scalar potentials in membrane, 5-brane, p-branes, multiple M2 branes, BLG and
ABJM theories. We also give a sufficient condition for discreteness of the
spectrum for supersymmmetric and non supersymmetric theories with a fermionic
contribution. We characterize then the spectral properties of different
theories: the BMN matrix model, the supermembrane with central charges and a
bound state of D2 with D0. We show that, while the first two models
have a purely discrete spectrum with finite multiplicity, the latter has a
continuous spectrum starting from a constant given in terms of the monopole
charge.Comment: 10pg, Latex, Contributions to the Conference XVI European Workshop on
String Theory 2010, Madrid June 14-18, 201
Convergence of U-statistics for interacting particle systems
The convergence of U-statistics has been intensively studied for estimators
based on families of i.i.d. random variables and variants of them. In most
cases, the independence assumption is crucial [Lee90, de99]. When dealing with
Feynman-Kac and other interacting particle systems of Monte Carlo type, one
faces a new type of problem. Namely, in a sample of N particles obtained
through the corresponding algorithms, the distributions of the particles are
correlated -although any finite number of them is asymptotically independent
with respect to the total number N of particles. In the present article,
exploiting the fine asymptotics of particle systems, we prove convergence
theorems for U-statistics in this framework
Arguments towards the construction of a matrix model groundstate
We discuss the existence and uniqueness of wavefunctions for inhomogenoeus
boundary value problems associated to x^2y^2-type matrix model on a bounded
domain of R^2. Both properties involve a combination of the Cauchy-Kovalewski
Theorem and a explicit calculations.Comment: 3 pages, Latex Proceedings for the XIX Simposio Chileno de Fisica,
SOCHIFI 2014 Conference, 26-28 November 2014, held at Concepcion U., Chil
On the groundstate of octonionic matrix models in a ball
In this work we examine the existence and uniqueness of the groundstate of a
SU(N)x G2 octonionic matrix model on a bounded domain of R^N. The existence and
uniqueness argument of the groundstate wavefunction follows from the
Lax-Milgram theorem. Uniqueness is shown by means of an explicit argument which
is drafted in some detail.Comment: Latex, 6 page
On the Stability and the Approximation of Branching Distribution Flows, with Applications to Nonlinear Multiple Target Filtering
We analyse the exponential stability properties of a class of measure-valued
equations arising in nonlinear multi-target filtering problems. We also prove
the uniform convergence properties w.r.t. the time parameter of a rather
general class of stochastic filtering algorithms, including sequential Monte
Carlo type models and mean eld particle interpretation models. We illustrate
these results in the context of the Bernoulli and the Probability Hypothesis
Density filter, yielding what seems to be the first results of this kind in
this subject
The supermembrane with central charges:(2+1)-D NCSYM, confinement and phase transition
The spectrum of the bosonic sector of the D=11 supermembrane with central
charges is shown to be discrete and with finite multiplicities, hence
containing a mass gap. The result extends to the exact theory our previous
proof of the similar property for the SU(N) regularised model and strongly
suggest discreteness of the spectrum for the complete Hamiltonian of the
supermembrane with central charges. This theory is a quantum equivalent to a
symplectic non-commutative super-Yang-Mills in 2+1 dimensions, where the
space-like sector is a Riemann surface of positive genus. In this context, it
is argued how the theory in 4D exhibits confinement in the N=1 supermembrane
with central charges phase and how the theory enters in the quark-gluon plasma
phase through the spontaneous breaking of the centre. This phase is interpreted
in terms of the compactified supermembrane without central charges.Comment: 33 pages, Latex. In this new version, several changes have been made
and various typos were correcte
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