980 research outputs found
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
A Backward Particle Interpretation of Feynman-Kac Formulae
We design a particle interpretation of Feynman-Kac measures on path spaces
based on a backward Markovian representation combined with a traditional mean
field particle interpretation of the flow of their final time marginals. In
contrast to traditional genealogical tree based models, these new particle
algorithms can be used to compute normalized additive functionals "on-the-fly"
as well as their limiting occupation measures with a given precision degree
that does not depend on the final time horizon.
We provide uniform convergence results w.r.t. the time horizon parameter as
well as functional central limit theorems and exponential concentration
estimates. We also illustrate these results in the context of computational
physics and imaginary time Schroedinger type partial differential equations,
with a special interest in the numerical approximation of the invariant measure
associated to -processes
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
On the spectrum of a matrix model for the D=11 supermembrane compactified on a torus with non-trivial winding
The spectrum of the Hamiltonian of the double compactified D=11 supermembrane
with non-trivial central charge or equivalently the non-commutative symplectic
super Maxwell theory is analyzed. In distinction to what occurs for the D=11
supermembrane in Minkowski target space where the bosonic potential presents
string-like spikes which render the spectrum of the supersymmetric model
continuous, we prove that the potential of the bosonic compactified membrane
with non-trivial central charge is strictly positive definite and becomes
infinity in all directions when the norm of the configuration space goes to
infinity. This ensures that the resolvent of the bosonic Hamiltonian is
compact. We find an upper bound for the asymptotic distribution of the
eigenvalues.Comment: 11 pages, LaTe
Degenerate neutrinos from a supersymmetric A_4 model
We investigate the supersymmetric A_4 model recently proposed by Babu, Ma and
Valle. The model naturally gives quasi-degenerate neutrinos that are bi-largely
mixed, in agreement with observations. Furthermore, the mixings in the quark
sector are constrained to be small, making it a complete model of the flavor
structure. Moreover, it has the interesting property that CP-violation in the
leptonic sector is maximal (unless vanishing). The model exhibit a close
relation between the slepton and lepton sectors and we derive the slepton
spectra that are compatible with neutrino data and the present bounds on
flavor-violating charged lepton decays. The prediction for the branching ratio
of the decay tau -> mu gamma has a lower limit of 10^{-9}. In addition, the
overall neutrino mass scale is constrained to be larger than 0.3 eV. Thus, the
model will be tested in the very near future.Comment: 11 pages, 6 figures. Talk given at the International Workshop on
Astroparticle and High Energy Physics (AHEP), Valencia, Spain, 14-18 Oct.
200
On Chern-Simons Quivers and Toric Geometry
We discuss a class of 3-dimensional N=4 Chern-Simons (CS) quiver gauge models
obtained from M-theory compactifications on singular complex 4-dimensional
hyper-Kahler (HK) manifolds, which are realized explicitly as a cotangent
bundle over two-Fano toric varieties V^2. The corresponding CS gauge models are
encoded in quivers similar to toric diagrams of V^2. Using toric geometry, it
is shown that the constraints on CS levels can be related to toric equations
determining V^2.Comment: 14pg, 1 Figure, late
Forest resampling for distributed sequential Monte Carlo
This paper brings explicit considerations of distributed computing
architectures and data structures into the rigorous design of Sequential Monte
Carlo (SMC) methods. A theoretical result established recently by the authors
shows that adapting interaction between particles to suitably control the
Effective Sample Size (ESS) is sufficient to guarantee stability of SMC
algorithms. Our objective is to leverage this result and devise algorithms
which are thus guaranteed to work well in a distributed setting. We make three
main contributions to achieve this. Firstly, we study mathematical properties
of the ESS as a function of matrices and graphs that parameterize the
interaction amongst particles. Secondly, we show how these graphs can be
induced by tree data structures which model the logical network topology of an
abstract distributed computing environment. Thirdly, we present efficient
distributed algorithms that achieve the desired ESS control, perform resampling
and operate on forests associated with these trees
Transverse momentum fluctuations and percolation of strings
The behaviour of the transverse momentum fluctuations with the centrality of
the collision shown by the Relativistic Heavy Ion Collider data is naturally
explained by the clustering of color sources. In this framework, elementary
color sources --strings-- overlap forming clusters, so the number of effective
sources is modified. These clusters decay into particles with mean transverse
momentum that depends on the number of elementary sources that conform each
cluster, and the area occupied by the cluster. The transverse momentum
fluctuations in this approach correspond to the fluctuations of the transverse
momentum of these clusters, and they behave essentially as the number of
effective sources.Comment: 16 pages, RevTex, 4 postscript figures. Enhanced version. New figure
Supersymmetric exact sequence, heat kernel and super KdV hierarchy
We introduce the free N=1 supersymmetric derivation ring and prove the
existence of an exact sequence of supersymmetric rings and linear
transformations. We apply necessary and sufficient conditions arising from this
exact supersymmetric sequence to obtain the essential relations between
conserved quantities, gradients and the N=1 super KdV hierarchy. We combine
this algebraic approach with an analytic analysis of the super heat operator.We
obtain the explicit expression for the Green's function of the super heat
operator in terms of a series expansion and discuss its properties. The
expansion is convergent under the assumption of bounded bosonic and fermionic
potentials. We show that the asymptotic expansion when of the Green's
function for the super heat operator evaluated over its diagonal generates all
the members of the N=1 super KdV hierarchy.Comment: 20 pages, to be published in JM
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