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

A note on a Mar\v{c}enko-Pastur type theorem for time series

In this note we develop an extension of the Mar\v{c}enko-Pastur theorem to time series model with temporal correlations. The limiting spectral distribution (LSD) of the sample covariance matrix is characterised by an explicit equation for its Stieltjes transform depending on the spectral density of the time series. A numerical algorithm is then given to compute the density functions of these LSD's

Strong consistency of the maximum likelihood estimator for finite mixtures of location-scale distributions when penalty is imposed on the ratios of the scale parameters

In finite mixtures of location-scale distributions, if there is no constraint or penalty on the parameters, then the maximum likelihood estimator does not exist because the likelihood is unbounded. To avoid this problem, we consider a penalized likelihood, where the penalty is a function of the minimum of the ratios of the scale parameters and the sample size. It is shown that the penalized maximum likelihood estimator is strongly consistent. We also analyze the consistency of a penalized maximum likelihood estimator where the penalty is imposed on the scale parameters themselves.Comment: 29 pages, 2 figure

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

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

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

On a certain class of semigroups of operators

We define an interesting class of semigroups of operators in Banach spaces, namely, the randomly generated semigroups. This class contains as a remarkable subclass a special type of quantum dynamical semigroups introduced by Kossakowski in the early 1970s. Each randomly generated semigroup is associated, in a natural way, with a pair formed by a representation or an antirepresentation of a locally compact group in a Banach space and by a convolution semigroup of probability measures on this group. Examples of randomly generated semigroups having important applications in physics are briefly illustrated.Comment: 11 page

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

Additivity properties of a Gaussian Channel

The Amosov-Holevo-Werner conjecture implies the additivity of the minimum Re'nyi entropies at the output of a channel. The conjecture is proven true for all Re'nyi entropies of integer order greater than two in a class of Gaussian bosonic channel where the input signal is randomly displaced or where it is coupled linearly to an external environment.Comment: 9 pages, 1 figure (minor error present in the published version corrected