The effect of round-off error on long memory processes

We study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequently, we find that the discretized process is also long memory with the same Hurst exponent as the original process. We consider the properties of two estimators of the Hurst exponent, namely the local Whittle (LW) estimator and the Detrended Fluctuation Analysis (DFA). By using analytical considerations and numerical simulations we show that, in presence of round-off error, both estimators are severely negatively biased in finite samples. Under regularity conditions we prove that the LW estimator applied to discretized processes is consistent and asymptotically normal. Moreover, we compute the asymptotic properties of the DFA for a generic (i.e. non Gaussian) long memory process and we apply the result to discretized processes.Comment: 44 pages, 4 figures, 4 table

Competition, reach for yield, and money market funds

Do asset managers reach for yield because of competitive pressures in a low-rate environment? I propose a tournament model of money market funds (MMFs) to study this issue. When funds care about relative performance, an increase in the risk premium leads funds with lower default costs to increase risk-taking, while funds with higher default costs decrease risk-taking. Without changes in the premium, lower risk-free rates reduce the risk-taking of all funds. I show that these predictions are consistent with MMF risk-taking during the 2002-08 period and that rank-based performance is indeed a key determinant of money flows to MMFs

CP Violation Tests of Alignment Models at LHCII

We analyse the low-energy phenomenology of alignment models both model-independently and within supersymmetric (SUSY) scenarios focusing on their CP violation tests at LHCII. Assuming that New Physics (NP) contributes to K-Kbar and D-Dbar mixings only through non-renormalizable operators involving SU(2)_L quark-doublets, we derive model-independent correlations among CP violating observables of the two systems. Due to universality of CP violation in Delta F=1 processes the bound on CP violation in Kaon mixing generically leads to an upper bound on the size of CP violation in D mixing. Interestingly, this bound is similar in magnitude to the current sensitivity reached by the LHCb experiment which is starting now to probe the natural predictions of alignment models. Within SUSY, we perform an exact analytical computation of the full set of contributions for the D-Dbar mixing amplitude. We point out that chargino effects are comparable and often dominant with respect to gluino contributions making their inclusion in phenomenological analyses essential. As a byproduct, we clarify the limit of applicability of the commonly used mass insertion approximation in scenarios with quasi-degenerate and split squarks.Comment: 26 pages, 5 figure

Self-Dualities and Renormalization Dependence of the Phase Diagram in 3d O(N)O(N) Vector Models

In the classically unbroken phase, 3d $O(N)$ symmetric $\phi^4$ vector models admit two equivalent descriptions connected by a strong-weak duality closely related to the one found by Chang and Magruder long ago. We determine the exact analytic renormalization dependence of the critical couplings in the weak and strong branches as a function of the renormalization scheme (parametrized by $\kappa$) and for any $N$. It is shown that for $\kappa=\kappa_*$ the two fixed points merge and then, for $\kappa<\kappa_*$, they move into the complex plane in complex conjugate pairs, making the phase transition no longer visible from the classically unbroken phase. Similar considerations apply in 2d for the $N=1$ $\phi^4$ theory, where the role of classically broken and unbroken phases is inverted. We verify all these considerations by computing the perturbative series of the 3d $O(N)$ models for the vacuum energy and for the mass gap up to order eight, and Borel resumming the series. In particular, we provide numerical evidence for the self-duality and verify that in renormalization schemes where the critical couplings are complex the theory is gapped. As a by-product of our analysis, we show how the non-perturbative mass gap at large $N$ in 2d can be seen as the analytic continuation of the perturbative one in the classically unbroken phase.Comment: 38 pages, 12 figures; v3: version to appear in JHE

Attractive Solution of Binary Bose Mixtures: Liquid-Vapor Coexistence and Critical Point

We study the thermodynamic behavior of attractive binary Bose mixtures using exact path-integral Monte-Carlo methods. Our focus is on the regime of interspecies interactions where the ground state is in a self-bound liquid phase, stabilized by beyond mean-field effects. We calculate the isothermal curves in the pressure vs density plane for different values of the attraction strength and establish the extent of the coexistence region between liquid and vapor using the Maxwell construction. Notably, within the coexistence region, Bose-Einstein condensation occurs in a discontinuous way as the density jumps from the normal gas to the superfluid liquid phase. Furthermore, we determine the critical point where the line of first-order transition ends and investigate the behavior of the density discontinuity in its vicinity. We also point out that the density discontinuity at the transition could be observed in experiments of mixtures in traps.Comment: v1: 6 pages, 5 figures. Supplemental material: 4 pages, 2 figures. Data available on zenodo.org; v2: minor improvements, matches PRL published versio

Self-Dualities and Renormalization Dependence of the Phase Diagram in 3d O(N)O(N) Vector Models

In the classically unbroken phase, 3d O(N) symmetric phi (4) vector models admit two equivalent descriptions connected by a strong-weak duality closely related to the one found by Chang and Magruder long ago. We determine the exact analytic renormalization dependence of the critical couplings in the weak and strong branches as a function of the renormalization scheme (parametrized by kappa) and for any N. It is shown that for kappa = kappa the two fixed points merge and then, for kappa &lt; , they move into the complex plane in complex conjugate pairs, making the phase transition no longer visible from the classically unbroken phase. Similar considerations apply in 2d for the N = 1 phi (4) theory, where the role of classically broken and unbroken phases is inverted. We verify all these considerations by computing the perturbative series of the 3d O(N) models for the vacuum energy and for the mass gap up to order eight, and Borel resumming the series. In particular, we provide numerical evidence for the self-duality and verify that in renormalization schemes where the critical couplings are complex the theory is gapped. As a by-product of our analysis, we show how the non-perturbative mass gap at large N in 2d can be seen as the analytic continuation of the perturbative one in the classically unbroken phase

Renormalization scheme dependence, RG flow, and Borel summability in phi^4 Theories in d<4

Renormalization group (RG) and resummation techniques have been used in N-component.4 theories at fixed dimensions below four to determine the presence of nontrivial IR fixed points and to compute the associated critical properties. Since the coupling constant is relevant in d &lt; 4 dimensions, the RG is entirely governed by renormalization scheme-dependent terms. We show that the known proofs of the Borel summability of observables depend on the renormalization scheme and apply only in "minimal" ones, equivalent in d = 2 to an operatorial normal ordering prescription, where the beta-function is trivial to all orders in perturbation theory. The presence of a nontrivial fixed point can be unambiguously established by considering a physical observable, like the mass gap, with no need of RG techniques. Focusing on the N = 1, d = 2.4 theory, we define a one-parameter family of renormalization schemes where Borel summability is guaranteed and study the accuracy on the determination of the critical exponent. as the scheme is varied. While the critical coupling shows a significant sensitivity on the scheme, the accuracy in. is essentially constant. As a by-product of our analysis, we improve the determination of. obtained with RG methods by computing three more orders in perturbation theory

The metacognitions about smoking questionnaire : development and psychometric properties

The Metacognitions about Smoking Questionnaire was shown to possess good psychometric properties, as well as predictive and divergent validity within the populations that were tested. The metacognition factors explained incremental variance in smoking behaviour above smoking outcome expectancies