A
bstract
We study the connection between many-body quantum chaos and energy dynamics for the holographic theory dual to the Kerr-AdS black hole. In particular, we determine a partial differential ...equation governing the angular profile of gravitational shock waves that are relevant for the computation of out-of-time ordered correlation functions (OTOCs). Further we show that this shock wave profile is directly related to the behaviour of energy fluctuations in the boundary theory. In particular, we demonstrate using the Teukolsky formalism that at complex frequency
ω
∗
=
i
2
πT
there exists an extra ingoing solution to the linearised Einstein equations whenever the angular profile of metric perturbations near the horizon satisfies this shock wave equation. As a result, for metric perturbations with such temporal and angular profiles we find that the energy density response of the boundary theory exhibit the signatures of “pole-skipping” — namely, it is undefined, but exhibits a collective mode upon a parametrically small deformation of the profile. Additionally, we provide an explicit computation of the OTOC in the equatorial plane for slowly rotating large black holes, and show that its form can be used to obtain constraints on the dispersion relations of collective modes in the dual CFT.
Space–time modelling of extreme events Huser, R; Davison, A. C
Journal of the Royal Statistical Society. Series B, Statistical methodology,
March 2014, Volume:
76, Issue:
2
Journal Article
Peer reviewed
Open access
Max‐stable processes are the natural analogues of the generalized extreme value distribution when modelling extreme events in space and time. Under suitable conditions, these processes are ...asymptotically justified models for maxima of independent replications of random fields, and they are also suitable for the modelling of extreme measurements over high thresholds. The paper shows how a pairwise censored likelihood can be used for consistent estimation of the extremes of space–time data under mild mixing conditions and illustrates this by fitting an extension of a model due to Schlather to hourly rainfall data. A block bootstrap procedure is used for uncertainty assessment. Estimator efficiency is considered and the choice of pairs to be included in the pairwise likelihood is discussed. The model proposed fits the data better than some natural competitors.
We present a theory of thermoelectric transport in weakly disordered Weyl semimetals where the electron–electron scattering time is faster than the electron–impurity scattering time. Our hydrodynamic ...theory consists of relativistic fluids at each Weyl node, coupled together by perturbatively small intervalley scattering, and long-range Coulomb interactions. The conductivity matrix of our theory is Onsager reciprocal and positive semidefinite. In addition to the usual axial anomaly, we account for the effects of a distinct, axial–gravitational anomaly expected to be present in Weyl semimetals. Negative thermal magnetoresistance is a sharp, experimentally accessible signature of this axial–gravitational anomaly, even beyond the hydrodynamic limit.
A
bstract
Recent developments have indicated that in addition to out-of-time ordered correlation functions (OTOCs), quantum chaos also has a sharp manifestation in the thermal energy density ...two-point functions, at least for maximally chaotic systems. The manifestation, referred to as pole-skipping, concerns the analytic behaviour of energy density two-point functions around a special point
ω
=
iλ
,
k
=
iλ/v
B
in the complex frequency and momentum plane. Here
λ
and
v
B
are the Lyapunov exponent and butterfly velocity characterising quantum chaos. In this paper we provide an argument that the phenomenon of pole-skipping is universal for general finite temperature systems dual to Einstein gravity coupled to matter. In doing so we uncover a surprising universal feature of the linearised Einstein equations around a static black hole geometry. We also study analytically a holographic axion model where all of the features of our general argument as well as the pole-skipping phenomenon can be verified in detail.
A
bstract
We explore a new class of general properties of thermal holographic Green’s functions that can be deduced from the near-horizon behaviour of classical perturbations in asymptotically ...anti-de Sitter spacetimes. We show that at negative imaginary Matsubara frequencies and appropriate complex values of the wavenumber the retarded Green’s functions of generic operators are not uniquely defined, due to the lack of a unique ingoing solution for the bulk perturbations. From a boundary perspective these ‘pole-skipping’ points correspond to locations in the complex frequency and momentum planes at which a line of poles of the retarded Green’s function intersects with a line of zeroes. As a consequence the dispersion relations of collective modes in the boundary theory at energy scales
ω ∼ T
are directly constrained by the bulk dynamics near the black-brane horizon. For the case of conserved U (1) current and energy-momentum tensor operators we give examples where the dispersion relations of hydrodynamic modes pass through a succession of pole- skipping points as real wavenumber is increased. We discuss implications of our results for transport, hydrodynamics and quantum chaos in holographic systems.
Genton et al. (2011) investigated the gain in efficiency when triplewise, rather than pairwise, likelihood is used to fit the popular Smith max-stable model for spatial extremes. We generalize their ...results to the Brown-Resnick model and show that the efficiency gain is substantial only for very smooth processes, which are generally unrealistic in applications.
Max-stable processes are increasingly widely used for modelling complex extreme events, but existing fitting methods are computationally demanding, limiting applications to a few dozen variables. ...r-Pareto processes are mathematically simpler and have the potential advantage of incorporating all relevant extreme events, by generalizing the notion of a univariate exceedance. In this paper we investigate the use of proper scoring rules for high-dimensional peaks-over-threshold inference, focusing on extreme-value processes associated with log-Gaussian random functions, and compare gradient score estimators with the spectral and censored likelihood estimators for regularly varying distributions with normalized marginals, using data with several hundred locations. When simulating from the true model, the spectral estimator performs best, closely followed by the gradient score estimator, but censored likelihood estimation performs better with simulations from the domain of attraction, though it is outperformed by the gradient score in cases of weak extremal dependence. We illustrate the potential and flexibility of our ideas by modelling extreme rainfall on a grid with 3600 locations, based on exceedances for locally intense and for spatially accumulated rainfall, and discuss diagnostics of model fit. The differences between the two fitted models highlight how the definition of rare events affects the estimated dependence structure.
The areal modeling of the extremes of a natural process such as rainfall or temperature is important in environmental statistics; for example, understanding extreme areal rainfall is crucial in flood ...protection. This article reviews recent progress in the statistical modeling of spatial extremes, starting with sketches of the necessary elements of extreme value statistics and geostatistics. The main types of statistical models thus far proposed, based on latent variables, on copulas and on spatial max-stable processes, are described and then are compared by application to a data set on rainfall in Switzerland. Whereas latent variable modeling allows a better fit to marginal distributions, it fits the joint distributions of extremes poorly, so appropriately-chosen copula or max-stable models seem essential for successful spatial modeling of extremes.
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