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On the asymptotic distribution of the mean absolute deviation about the meanJun 16 2014The mean absolute deviation about the mean is an alternative to the standard deviation for measuring dispersion in a sample or in a population. For stationary, ergodic time series with a finite first moment, an asymptotic expansion for the sample mean ... More

Hybrid Copula EstimatorsMay 08 2014Nov 28 2014An extension of the empirical copula is considered by combining an estimator of a multivariate cumulative distribution function with estimators of the marginal cumulative distribution functions for marginal estimators that are not necessarily equal to ... More

On the weak convergence of the empirical conditional copula under a simplifying assumptionNov 20 2015May 16 2017When the copula of the conditional distribution of two random variables given a covariate does not depend on the value of the covariate, two conflicting intuitions arise about the best possible rate of convergence attainable by nonparametric estimators ... More

Asymptotics of empirical copula processes under non-restrictive smoothness assumptionsDec 09 2010Jul 05 2012Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hypercube. The assumption is non-restrictive in the sense ... More

Multivariate regular variation of heavy-tailed Markov chainsJan 15 2007The upper extremes of a Markov chain with regulary varying stationary marginal distribution are known to exhibit under general conditions a multiplicative random walk structure called the tail chain. More generally, if the Markov chain is allowed to switch ... More

Max-stable models for multivariate extremesApr 02 2012Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models for univariate ... More

One- versus multi-component regular variation and extremes of Markov treesFeb 06 2019A Markov tree is a random vector indexed by the nodes of a tree whose distribution is determined by the distributions of pairs of neighbouring variables and a list of conditional independence relations. Upon an assumption on the tails of the Markov kernels ... More

Nonparametric Inference for Max-Stable DependenceAug 17 2012Discussion of "Statistical Modeling of Spatial Extremes" by A. C. Davison, S. A. Padoan and M. Ribatet [arXiv:1208.3378].

Generalised regular variation of arbitrary orderJan 11 2009Let $f$ be a measurable, real function defined in a neighbourhood of infinity. The function $f$ is said to be of generalised regular variation if there exist functions $h \not\equiv 0$ and $g > 0$ such that $f(xt) - f(t) = h(x) g(t) + o(g(t))$ as $t \to ... More

Regularly varying multivariate time seriesJul 26 2007Jul 26 2007A multivariate, stationary time series is said to be jointly regularly varying if all its finite-dimensional distributions are multivariate regularly varying. This property is shown to be equivalent to weak convergence of the conditional distribution ... More

Nonparametric estimation of multivariate extreme-value copulasJul 12 2011Nov 29 2011Extreme-value copulas arise in the asymptotic theory for componentwise maxima of independent random samples. An extreme-value copula is determined by its Pickands dependence function, which is a function on the unit simplex subject to certain shape constraints ... More

Nonparametric estimation of an extreme-value copula in arbitrary dimensionsOct 05 2009Inference on an extreme-value copula usually proceeds via its Pickands dependence function, which is a convex function on the unit simplex satisfying certain inequality constraints. In the setting of an iid random sample from a multivariate distribution ... More

Extreme-Value CopulasNov 05 2009Dec 07 2009Being the limits of copulas of componentwise maxima in independent random samples, extreme-value copulas can be considered to provide appropriate models for the dependence structure between rare events. Extreme-value copulas not only arise naturally in ... More

Extreme value copula estimation based on block maxima of a multivariate stationary time seriesNov 13 2013May 08 2014The core of the classical block maxima method consists of fitting an extreme value distribution to a sample of maxima over blocks extracted from an underlying series. In asymptotic theory, it is usually postulated that the block maxima are an independent ... More

Nonparametric estimation of the tree structure of a nested Archimedean copulaApr 04 2013Dec 17 2013One of the features inherent in nested Archimedean copulas, also called hierarchical Archimedean copulas, is their rooted tree structure. A nonparametric, rank-based method to estimate this structure is presented. The idea is to represent the target structure ... More

Markov tail chainsApr 29 2013Feb 03 2014The extremes of a univariate Markov chain with regulary varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper, we extend this fact to ... More

On the covariance of the asymptotic empirical copula processMar 19 2009Mar 16 2010Conditions are given under which the empirical copula process associated with a random sample from a bivariate continuous distribution has a smaller asymptotic covariance function than the standard empirical process based on observations from the copula. ... More

Tails of correlation mixtures of elliptical copulasDec 17 2009Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical copulas with the ... More

Marginal standardization of upper semicontinuous processes. With application to max-stable processesMar 14 2016In the field of spatial extremes, stochastic processes with upper semicontinuous (usc) trajectories have been proposed as random shape functions for max-stable models. In the literature dealing with usc processes, max-stability is defined via a sequences ... More

On the weak convergence of the empirical conditional copula under a simplifying assumptionNov 20 2015When the copula of the conditional distribution of two random variables given a covariate does not depend on the value of the covariate, two conflicting intuitions arise about the best possible rate of convergence attainable by nonparametric estimators ... More

Tails of multivariate Archimedean copulasJan 12 2009A complete and user-friendly directory of tails of Archimedean copulas is presented which can be used in the selection and construction of appropriate models with desired properties. The results are synthesized in the form of a decision tree: Given the ... More

Rank-based inference for bivariate extreme-value copulasJul 27 2007Aug 26 2009Consider a continuous random pair $(X,Y)$ whose dependence is characterized by an extreme-value copula with Pickands dependence function $A$. When the marginal distributions of $X$ and $Y$ are known, several consistent estimators of $A$ are available. ... More

On the maximum likelihood estimator for the Generalized Extreme-Value distributionJan 21 2016Oct 13 2016The vanilla method in univariate extreme-value theory consists of fitting the three-parameter Generalized Extreme-Value (GEV) distribution to a sample of block maxima. Despite claims to the contrary, the asymptotic normality of the maximum likelihood ... More

Maximum likelihood estimation for the Fréchet distribution based on block maxima extracted from a time seriesNov 24 2015Sep 16 2016The block maxima method in extreme-value analysis proceeds by fitting an extreme-value distribution to a sample of block maxima extracted from an observed stretch of a time series. The method is usually validated under two simplifying assumptions: the ... More

Regularly varying time series in Banach spacesJan 19 2010When a spatial process is recorded over time and the observation at a given time instant is viewed as a point in a function space, the result is a time series taking values in a Banach space. To study the spatio-temporal extremal dynamics of such a time ... More

Nonparametric estimation of pair-copula constructions with the empirical pair-copulaJan 24 2012A pair-copula construction is a decomposition of a multivariate copula into a structured system, called regular vine, of bivariate copulae or pair-copulae. The standard practice is to model these pair-copulae parametrically, which comes at the cost of ... More

Tails of random sums of a heavy-tailed number of light-tailed termsMar 01 2007Oct 09 2007The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the collective risk ... More

The Empirical Beta CopulaJul 15 2016Given a sample from a multivariate distribution $F$, the uniform random variates generated independently and rearranged in the order specified by the componentwise ranks of the original sample look like a sample from the copula of $F$. This idea can be ... More

Nonparametric Bayesian Inference on Bivariate ExtremesNov 17 2009May 11 2012The tail of a bivariate distribution function in the domain of attraction of a bivariate extreme-value distribution may be approximated by the one of its extreme-value attractor. The extreme-value attractor has margins that belong to a three-parameter ... More

The Empirical Beta CopulaJul 15 2016Nov 18 2016Given a sample from a multivariate distribution $F$, the uniform random variates generated independently and rearranged in the order specified by the componentwise ranks of the original sample look like a sample from the copula of $F$. This idea can be ... More

On the longest gap between power-rate arrivalsMar 28 2017Sep 21 2017Let $L_t$ be the longest gap before time $t$ in an inhomogeneous Poisson process with rate function $\lambda_t$ proportional to $t^{\alpha-1}$ for some $\alpha\in(0,1)$. It is shown that $\lambda_tL_t-b_t$ has a limiting Gumbel distribution for suitable ... More

An estimator of the stable tail dependence function based on the empirical beta copulaSep 12 2017The replacement of indicator functions by integrated beta kernels in the definition of the empirical stable tail dependence function is shown to produce a smoothed version of the latter estimator with the same asymptotic distribution but superior finite-sample ... More

A functional limit theorem for dependent sequences with infinite variance stable limitsJan 08 2010Oct 11 2012Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version of this is ... More

Multivariate peaks over thresholds modelsMar 21 2016May 03 2017Multivariate peaks over thresholds modeling based on generalized Pareto distributions has up to now only been used in few and mostly 2-dimensional situations. This paper contributes theoretical understanding, physically based models, inference tools, ... More

Multivariate peaks over thresholds modelsMar 21 2016Multivariate peaks over thresholds modeling based on generalized Pareto distributions has up to now only been used in few and mostly low-dimensional situations. This paper contributes to the theoretical understanding, physically based models, inference ... More

Second-order refined peaks-over-threshold modelling for heavy-tailed distributionsJan 12 2009Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit well and in such ... More

Large-sample tests of extreme-value dependence for multivariate copulasMay 11 2011Starting from the characterization of extreme-value copulas based on max-stability, large-sample tests of extreme-value dependence for multivariate copulas are studied. The two key ingredients of the proposed tests are the empirical copula of the data ... More

Polar decomposition of regularly varying time series in star-shaped metric spacesApr 01 2016Feb 02 2017There exist two ways of defining regular variation of a time series in a star-shaped metric space: either by the distributions of finite stretches of the series or by viewing the whole series as a single random element in a sequence space. The two definitions ... More

Risk Concentration and Diversification: Second-Order PropertiesOct 13 2009Dec 19 2009The quantification of diversification benefits due to risk aggregation plays a prominent role in the (regulatory) capital management of large firms within the financial industry. However, the complexity of today's risk landscape makes a quantifiable reduction ... More

Radial-angular decomposition of regularly varying time series in star-shaped metric spacesApr 01 2016There exist two ways of defining regular variation of a time series in a star-shaped metric space: either by the distributions of finite stretches of the series or by viewing the whole series as a single random element in a sequence space. The two definitions ... More

Statistics for Tail Processes of Markov ChainsMay 29 2014Dec 10 2014At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of the process ... More

Bayesian inference for bivariate ranksFeb 09 2018A recommender system based on ranks is proposed, where an expert's ranking of a set of objects and a user's ranking of a subset of those objects are combined to make a prediction of the user's ranking of all objects. The rankings are assumed to be induced ... More

When uniform weak convergence fails: Empirical processes for dependence functions and residuals via epi- and hypographsMay 28 2013Aug 14 2014In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions equipped with the ... More

Max-factor individual risk models with application to credit portfoliosDec 10 2014Individual risk models need to capture possible correlations as failing to do so typically results in an underestimation of extreme quantiles of the aggregate loss. Such dependence modelling is particularly important for managing credit risk, for instance, ... More

Multivariate peaks over thresholds modelsMar 21 2016Oct 20 2016Multivariate peaks over thresholds modeling based on generalized Pareto distributions has up to now only been used in few and mostly 2-dimensional situations. This paper contributes theoretical understanding, physically based models, inference tools, ... More

Nonparametric estimation of extremal dependenceNov 03 2014There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a multivariate distribution ... More

Maximum empirical likelihood estimation of the spectral measure of an extreme-value distributionDec 18 2008Sep 01 2009Consider a random sample from a bivariate distribution function $F$ in the max-domain of attraction of an extreme-value distribution function $G$. This $G$ is characterized by two extreme-value indices and a spectral measure, the latter determining the ... More

Detecting changes in cross-sectional dependence in multivariate time seriesJun 12 2012May 21 2014Classical and more recent tests for detecting distributional changes in multivariate time series often lack power against alternatives that involve changes in the cross-sectional dependence structure. To be able to detect such changes better, a test is ... More

Measuring Association between Random VectorsJul 21 2011This paper suggests five measures of association between two random vectors X = (X_1, ..., X_p) and Y = (Y_1, ..., Y_q). They are copula based and therefore invariant with respect to the marginal distributions of the components X_i and Y_j. The measures ... More

An M-estimator of spatial tail dependenceMar 08 2014Jan 09 2015Tail dependence models for distributions attracted to a max-stable law are fitted using observations above a high threshold. To cope with spatial, high-dimensional data, a rank-based M-estimator is proposed relying on bivariate margins only. A data-driven ... More

A method of moments estimator of tail dependenceOct 10 2007Nov 14 2008In the world of multivariate extremes, estimation of the dependence structure still presents a challenge and an interesting problem. A procedure for the bivariate case is presented that opens the road to a similar way of handling the problem in a truly ... More

A continuous updating weighted least squares estimator of tail dependence in high dimensionsJan 19 2016Likelihood-based procedures are a common way to estimate tail dependence parameters. They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can be hard to ... More

Peaks over thresholds modelling with multivariate generalized Pareto distributionsDec 06 2016The multivariate generalized Pareto distribution arises as the limit of a suitably normalized vector conditioned upon at least one component of that vector being extreme. Statistical modelling using multivariate generalized Pareto distributions constitutes ... More

Peaks over thresholds modelling with multivariate generalized Pareto distributionsDec 06 2016Feb 06 2018When assessing the impact of extreme events, it is often not just a single component, but the combined behaviour of several components which is important. Statistical modelling using multivariate generalized Pareto (GP) distributions constitutes the multivariate ... More

An M-estimator for tail dependence in arbitrary dimensionsDec 05 2011Oct 04 2012Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as the value ... More

Semiparametric Gaussian copula models: Geometry and efficient rank-based estimationJun 27 2013Oct 01 2014We propose, for multivariate Gaussian copula models with unknown margins and structured correlation matrices, a rank-based, semiparametrically efficient estimator for the Euclidean copula parameter. This estimator is defined as a one-step update of a ... More

A Sliding Blocks Estimator for the Extremal IndexDec 22 2008In extreme value statistics for stationary sequences, blocks estimators are usually constructed by using disjoint blocks because exceedances over high thresholds of different blocks can be assumed asymptotically independent. In this paper we focus on ... More

A Euclidean likelihood estimator for bivariate tail dependenceApr 16 2012The spectral measure plays a key role in the statistical modeling of multivariate extremes. Estimation of the spectral measure is a complex issue, given the need to obey a certain moment condition. We propose a Euclidean likelihood-based estimator for ... More

$L^p$-estimates for a transmission problem of mixed elliptic-parabolic typeNov 22 2013We consider the situation when an elliptic problem in a subdomain $\Omega_1$ of an $n$-dimensional bounded domain $\Omega$ is coupled via inhomogeneous canonical transmission conditions to a parabolic problem in $\Omega\setminus\Omega_1$. In particular, ... More

Connected, Disconnected and Strange Quark Contributions to HVPSep 06 2016We calculate all neutral vector two-point functions in Chiral Perturbation Theory (ChPT) to two-loop order and use these to estimate the ratio of disconnected to connected contributions as well as contributions involving the strange quark. We extend the ... More

The limit space of a Cauchy sequence of globally hyperbolic spacetimesAug 22 2003Nov 18 2003In this second paper, I construct a limit space of a Cauchy sequence of globally hyperbolic spacetimes. In the second section, I work gradually towards a construction of the limit space. I prove the limit space is unique up to isometry. I als show that, ... More

Radiative and semileptonic decays in Chiral Perturbation TheoryJul 03 2007I give a short overview of what has been done in radiative and semileptonic Kaon decays in Chiral Perturbation Theory. This includes for semileptonic decays the work which has been done to order $p^6$ including preliminary results of isospin breaking ... More

Eta and Eta' physicsOct 22 2007This talk describes the reasons why $\eta$ and $\eta^\prime$ decays are an interesting topic of study for both theory and experiment. The main part discusses the results of the recent calculation of $\eta\to3\pi$ at two-loop order in ChPT. Some puzzling ... More

QCD and Weak Interactions of Light QuarksApr 05 2002This review contains an overview of strong interaction effects in weak decays starting with a historical introduction. It contains a short overview of semileptonic decays and their relevance for measuring CKM matrix elements. The main part is devoted ... More

I : Chiral Perturbation for Kaons II: The $ΔI=1/2$-rule in the Chiral LimitJul 27 1999I : Chiral Perturbation Theory is introduced and its applications to semileptonic and nonleptonic kaon decays are discussed. II: The method of large $N_c$ is used to calculate $K\to\pi\pi$ nonleptonic matrix elements, in particular the matching procedure ... More

Chiral Perturbation TheoryFeb 27 1995A short overview of the current state of Chiral Perturbation Theory is given. This includes a description of the basic assumptions, the usefulness of the external field method is emphasized using a simple lowest order example. Then at next-to-leading ... More

An improved description of charged Higgs boson productionOct 11 2004Many extensions of the Standard Model predict the existence of charged Higgs bosons. In order to be able to find those particles, an accurate description of their production is needed. In Monte Carlo simulations of charged Higgs boson production at hadron ... More

The overhand shuffle mixes in $Θ(n^2\log n)$ stepsJan 24 2005Mar 14 2006The overhand shuffle is one of the ``real'' card shuffling methods in the sense that some people actually use it to mix a deck of cards. A mathematical model was constructed and analyzed by Pemantle [J. Theoret. Probab. 2 (1989) 37--49] who showed that ... More

Turan's problem 10 revisitedSep 11 2006Jun 28 2007In this paper we prove that inf_{|z_k| => 1} max_{v=1,...,n^2} |sum_{k=1}^n z_k^v| = sqrt n+O(n^{0.2625+epsilon}). This improves on the bound O(sqrt (n log n)) of Erdos and Renyi. In the special case of $n+1$ being a prime we have previously proved the ... More

Aspects of nonrelativistic quantum gravityOct 22 2009A nonrelativistic approach to quantum gravity is studied. At least for weak gravitational fields it should be a valid approximation. Such an approach can be used to point out problems and prospects inherent in a more exact theory of quantum gravity, yet ... More

Newtonian Quantum GravityDec 04 2006A Newtonian approach to quantum gravity is studied. At least for weak gravitational fields it should be a valid approximation. Such an approach could be used to point out problems and prospects inherent in a more exact theory of quantum gravity, yet to ... More

A hierarchy of cosmic compact objects - without black holesMar 14 2006We make the case for the existence of a, hitherto unknown and unobserved, hierarchy of ever more compact cosmic objects in the universe. This hypothesis is based on i) the assumption of "elementary" particle sub-constituents on several levels below the ... More

A simple solution to color confinementNov 03 2000We show that color confinement is a direct result of the nonabelian, i.e. nonlinear, nature of the color interaction in quantum chromodynamics. This makes it in general impossible to describe the color field as a collection of elementary quanta (gluons). ... More

Reply to comment on ``A simple explanation of the non-appearance of physical gluons and quarks"Feb 13 2003This is the reply to a comment by Andreas Aste [hep-th/0302103] on a previous article of mine in Can.J.Phys. The counter-arguments used by Aste utilize a mathematical limit without physical meaning. We still contend that in QCD, the particles ``gluons'' ... More

Operations and single particle interferometryDec 15 2003Jan 16 2006Interferometry of single particles with internal degrees of freedom is investigated. We discuss the interference patterns obtained when an internal state evolution device is inserted into one or both the paths of the interferometer. The interference pattern ... More

Replica Symmetry and Combinatorial OptimizationAug 13 2009Dec 01 2009We establish the soundness of the replica symmetric ansatz introduced by M. Mezard and G. Parisi for minimum matching and the traveling salesman problem in the pseudo-dimension d mean field model for d\geq 1. The case d=1 of minimum matching corresponds ... More

On the zeta function on the line Re(s) = 1Jul 18 2012We show the estimates \inf_T \int_T^{T+\delta} |\zeta(1+it)|^{-1} dt =e^{-\gamma}/4 \delta^2+ O(\delta^4) and \inf_T \int_T^{T+\delta} |\zeta(1+it)| dt =e^{-\gamma} \pi^2/24 \delta^2+ O(\delta^4) as well as corresponding results for sup-norm, L^p-norm ... More

Word-level Symbolic Trajectory EvaluationMay 29 2015Symbolic trajectory evaluation (STE) is a model checking technique that has been successfully used to verify industrial designs. Existing implementations of STE, however, reason at the level of bits, allowing signals to take values in {0, 1, X}. This ... More

The functional calculus for regular operators in Hilbert C*-modules revisitedJun 20 1997Woronowicz introduced the functional calculus for normal operators in Hilbert C*-modules. The aim of this paper is to translate, if possible, some basic properties of the functional calculus in Hilbert spaces to the Hilbert C*-module framework.

Universal C*-algebraic quantum groups arising from algebraic quantum groupsApr 22 1997In this paper, we construct a universal C*-algebraic quantum group out of an algebraic one. We show that this universal C*-algebraic quantum group has the same rich structure as its reduced companion. This universal C*-algebraic quantum group also satifies ... More

A natural extension of a left invariant lower semi-continuous weightApr 21 1997In this paper, we describe a natural method to extend left invariant weights on C*-algebraic quantum groups. This method is then used to improve the left invariance property of a left invariant weight. We also prove some kind of uniqueness result for ... More

Models of Low Energy Effective Theory applied to Kaon Non-leptonic Decays and Other Matrix ElementsOct 20 1999In this talk I describe work on computing non-leptonic matrix elements consistently with both long and short distance contributions included. On the simpler example of the $\pi^+$-$\pi^0$ mass difference I explain in detail the matching procedure and ... More

Introduction to Extended Nambu-Jona-Lasinio ModelsJun 30 1994A short introduction to quark models with four fermion terms and their predictions for the parameters of low-energy effective Lagrangians is given. Special attention is paid to predictions that are as general as possible. Contribution to the Second DAPHNE ... More

Chiral Perturbation Theory Beyond One LoopApr 05 2006Aug 01 2006The existing Chiral Perturbation Theory (ChPT) calculations at order $p^6$ are reviewed. The principles of ChPT and how they are used are introduced. The main part is a review of the two- and three-flavour full two-loop calculations and their comparison ... More

Chiral Perturbation Theory at Two Loops and the Measurement of $V_{us}$Apr 30 2003I give an overview of the calculations done in three-flavour Chiral perturbation theory at next-to-next-to-leading order with an emphasis on those relevant for an improvement in the accuracy of the measurement of $V_{us}$. It is pointed out that all needed ... More

Sea Quark Asymmetries in the Nucleon - A physical model for parton distributions in hadronsDec 20 2004A physical model for parton densities in hadrons, based on Gaussian momentum fluctuations of partons and hadronic baryon-meson fluctuations, is presented. The model has previously been shown to describe proton structure function data, and is now applied ... More

Quark Asymmetries in NucleonsJun 21 2005We have developed a physical model for the non-perturbative x-shape of parton density functions in the proton, based on Gaussian fluctuations in momenta, and quantum fluctuations of the proton into meson-baryon pairs. The model describes the proton structure ... More

Independence Complexes of Cylinders Constructed from Square and Hexagonal Grid GraphsDec 05 2008Fendley, Schoutens and van Eerten [Fendley et al., J. Phys. A: Math. Gen., 38 (2005), pp. 315-322] studied the hard square model at negative activity. They found analytical and numerical evidence that the eigenvalues of the transfer matrix with periodic ... More

Explicit solutions to certain inf max problems from Turan power sum theoryJul 10 2006Apr 04 2007Let s_v denote the pure power sum \sum_{k=1}^n z_k^v. In a previous paper we proved that \sqrt n <= \inf_{|z_k| => 1} \max_{v=1,...,n^2} |s_v| <= \sqrt{n+1} when n+1 is prime. In this paper we prove that \inf_{|z_k| = 1} \max_{v=1,...,n^2-n} |s_v| = \sqrt{n-1} ... More

On some power sum problems of Montgomery and TuranJun 28 2007Jul 11 2007We use an estimate for character sums over finite fields of Katz to solve open problems of Montgomery and Turan. Let h=>2 be an integer. We prove that inf_{|z_k| => 1} max_{v=1,...,n^h} |sum_{k=1}^n z_k^v| <= (h-1+o(1)) sqrt n. This gives the right order ... More

The "proton spin crisis" - a quantum queryApr 23 2003The "proton spin crisis" was introduced in the late 1980s, when the EMC-experiment revealed that little or nothing of a proton's spin seemed to be carried by its quarks. The main objective of this paper is to point out that it is wrong to assume that ... More

Nonlinear gauge interactions - A solution to the "measurement problem" in quantum mechanics?Mar 20 2000We propose that the mechanism responsible for the ``collapse of the wave function" (or "decoherence" in its broadest meaning) in quantum mechanics is the nonlinearities already present in the theory via nonabelian gauge interactions. Unlike all other ... More

Card-cyclic-to-random shuffling with relabelingJan 22 2015Sep 28 2015The card-cyclic-to-random shuffle is the card shuffle where the $n$ cards are labeled $1,\ldots,n$ according to their starting positions. Then the cards are mixed by first picking card $1$ from the deck and reinserting it at a uniformly random position, ... More

Generalized Gravity I : Kinematical Setting and reformalizing Quantum Field TheoryJan 28 2008Apr 20 2008The first part of this work deals with the development of a natural differential calculus on non-commutative manifolds. The second part extends the covariance and equivalence principle as well studies its kinematical consequences such as the arising of ... More

Lorentzian Gromov Hausdorff theory as a tool for quantum gravity kinematicsJan 30 2004This thesis start by a review of different approaches to classical and quantum gravity. The main theme is Lorentzian Gromov Hausdorff theory which is an active diffeomorphism invariant theory on the space of Lorentz spaces (think about globally hyperbolic ... More

KMS-weights on C*-algebrasApr 29 1997In this paper, we build a solid framework for KMS-weights on C*-algebras. We use another definition than the one introduced by Combes, but prove that they are equivalent.

The $ΔI=1/2$ rule and other matrix elementsOct 07 1999Recent work by J.Prades and myself on $K\to\pi\pi$ is described. The method we use to consistently connect long and short distances is described and numerical results for the $\Delta I=1/2$ rule and on $B_6$, the parameter relevant for the strong part ... More

Progress in $K\toππ$ DecaysJul 12 1999Recent work by J.~Prades and myself on $K\to\pi\pi$ is described. The first part describes our method to connect in a systematic fashion the short-distance evolution with long-distance matrix-element calculations taking the scheme dependence of the short-distance ... More

Goldstone Boson Production and DecayOct 14 1997Various topics in and around Goldstone Boson Production and Decay in CHPT are discussed, in particular I describe some of the progress in $p^6$ Chiral Perturbation Theory Calculations, the progress in calculating hadronic contributions to the muon anomalous ... More

Quark Mass dependence at Two Loops for Meson PropertiesAug 10 2007Aug 28 2007This talks contains a short introduction to Chiral Perturbation Theory and the existing calculations to two-loop order in the mesonic sector. I include a discussion on which quantities the expansion can be organized in. The present best values of the ... More