584 research outputs found
Brownian semistationary processes and conditional full support
In this note, we study the infinite-dimensional conditional laws of Brownian
semistationary processes. Motivated by the fact that these processes are
typically not semimartingales, we present sufficient conditions ensuring that a
Brownian semistationary process has conditional full support, a property
introduced by Guasoni, R\'asonyi, and Schachermayer [Ann. Appl. Probab., 18
(2008) pp. 491--520]. By the results of Guasoni, R\'asonyi, and Schachermayer,
this property has two important implications. It ensures, firstly, that the
process admits no free lunches under proportional transaction costs, and
secondly, that it can be approximated pathwise (in the sup norm) by
semimartingales that admit equivalent martingale measures.Comment: 7 page
Non existence of a phase transition for the Penetrable Square Wells in one dimension
Penetrable Square Wells in one dimension were introduced for the first time
in [A. Santos et. al., Phys. Rev. E, 77, 051206 (2008)] as a paradigm for
ultra-soft colloids. Using the Kastner, Schreiber, and Schnetz theorem [M.
Kastner, Rev. Mod. Phys., 80, 167 (2008)] we give strong evidence for the
absence of any phase transition for this model. The argument can be generalized
to a large class of model fluids and complements the van Hove's theorem.Comment: 14 pages, 7 figures, 1 tabl
Hypothesis testing for Gaussian states on bosonic lattices
The asymptotic state discrimination problem with simple hypotheses is
considered for a cubic lattice of bosons. A complete solution is provided for
the problems of the Chernoff and the Hoeffding bounds and Stein's lemma in the
case when both hypotheses are gauge-invariant Gaussian states with
translation-invariant quasi-free parts.Comment: 22 pages, submitted versio
Semiparametric sieve-type generalized least squares inference
This article considers the problem of statistical inference in linear regression models with dependent errors. A sieve-type generalized least squares (GLS) procedure is proposed based on an autoregressive approximation to the generating mechanism of the errors. The asymptotic properties of the sieve-type GLS estimator are established under general conditions, including mixingale-type conditions as well as conditions which allow for long-range dependence in the stochastic regressors and/or the errors. A Monte Carlo study examines the finite-sample properties of the method for testing regression hypotheses
Entanglement and criticality in translational invariant harmonic lattice systems with finite-range interactions
We discuss the relation between entanglement and criticality in
translationally invariant harmonic lattice systems with non-randon,
finite-range interactions. We show that the criticality of the system as well
as validity or break-down of the entanglement area law are solely determined by
the analytic properties of the spectral function of the oscillator system,
which can easily be computed. In particular for finite-range couplings we find
a one-to-one correspondence between an area-law scaling of the bi-partite
entanglement and a finite correlation length. This relation is strict in the
one-dimensional case and there is strog evidence for the multi-dimensional
case. We also discuss generalizations to couplings with infinite range.
Finally, to illustrate our results, a specific 1D example with nearest and
next-nearest neighbor coupling is analyzed.Comment: 4 pages, one figure, revised versio
Entanglement of Collectively Interacting Harmonic Chains
We study the ground-state entanglement of one-dimensional harmonic chains
that are coupled to each other by a collective interaction as realized e.g. in
an anisotropic ion crystal. Due to the collective type of coupling, where each
chain interacts with every other one in the same way,the total system shows
critical behavior in the direction orthogonal to the chains while the isolated
harmonic chains can be gapped and non-critical. We derive lower and most
importantly upper bounds for the entanglement,quantified by the von Neumann
entropy, between a compact block of oscillators and its environment. For
sufficiently large size of the subsystems the bounds coincide and show that the
area law for entanglement is violated by a logarithmic correction.Comment: 5 pages, 1 figur
Averaged Template Matching Equations
By exploiting an analogy with averaging procedures in fluid
dynamics, we present a set of averaged template matching equations.
These equations are analogs of the exact template matching equations
that retain all the geometric properties associated with the diffeomorphismgrou
p, and which are expected to average out small scale features
and so should, as in hydrodynamics, be more computationally efficient
for resolving the larger scale features. Froma geometric point of view,
the new equations may be viewed as coming from a change in norm that
is used to measure the distance between images. The results in this paper
represent first steps in a longer termpro gram: what is here is only
for binary images and an algorithm for numerical computation is not
yet operational. Some suggestions for further steps to develop the results
given in this paper are suggested
Topologies of nodal sets of random band limited functions
It is shown that the topologies and nestings of the zero and nodal sets of
random (Gaussian) band limited functions have universal laws of distribution.
Qualitative features of the supports of these distributions are determined. In
particular the results apply to random monochromatic waves and to random real
algebraic hyper-surfaces in projective space.Comment: 62 pages. Major revision following referee repor
Mixture of Kernels and Iterated Semidirect Product of Diffeomorphisms Groups
In the framework of large deformation diffeomorphic metric mapping (LDDMM),
we develop a multi-scale theory for the diffeomorphism group based on previous
works. The purpose of the paper is (1) to develop in details a variational
approach for multi-scale analysis of diffeomorphisms, (2) to generalise to
several scales the semidirect product representation and (3) to illustrate the
resulting diffeomorphic decomposition on synthetic and real images. We also
show that the approaches presented in other papers and the mixture of kernels
are equivalent.Comment: 21 pages, revised version without section on evaluatio
Algebraic reduction of the Ising model
We consider the Ising model on a cylindrical lattice of L columns, with
fixed-spin boundary conditions on the top and bottom rows. The spontaneous
magnetization can be written in terms of partition functions on this lattice.
We show how we can use the Clifford algebra of Kaufman to write these partition
functions in terms of L by L determinants, and then further reduce them to m by
m determinants, where m is approximately L/2. In this form the results can be
compared with those of the Ising case of the superintegrable chiral Potts
model. They point to a way of calculating the spontaneous magnetization of that
more general model algebraically.Comment: 25 pages, one figure, last reference completed. Various typos fixed.
Changes on 12 July 2008: Fig 1, 0 to +1; before (2.1), if to is; after (4.6),
from to form; before (4.46), first three to middle two; before (4.46), last
to others; Conclusions, 2nd para, insert how ; renewcommand \i to be \rm
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