2,059 research outputs found

    Gelfand–Tsetlin polytopes and random contractions away from the limiting shape.

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    In this paper, we consider a sequence of selfadjoint matrices An having a limiting spectral distribution as n → ∞, and we consider a sequence of full flags {0 ≤ p₁(n) ≤ ... ≤ pi(n) ≤ ... ≤ 1n} chosen at random according to the uniform measure on full flag manifolds. We are interested in the behaviour of the extremal eigenvalues of pi(n)Anpi(n). This problem is known to be equivalent to the study of uniform probability measures on Gelfand–Tsetlin polytopes. Our main results consist in explicit uniform estimates for extremal eigenvalues, and the fact that an outlier behavior has an exponentially small probability. This problem is of intrinsic interest in random matrix theory, but it was motivated from a problem in Quantum Information Theory, which we discuss. The proofs rely on a reinterpretation of the problem with the help of determinantal point processes and the techniques are based on steepest descent analysis.Dans cet article, nous nous intéressons à une suite de matrices autoadjointes An possédant une distribution spectrale lorsque n → ∞, et nous étudions une suite de drapeaux complets {0 ≤ p₁(n) ≤ ... ≤ pi(n) ≤ ... ≤ 1n} choisis au hasard selon la loi uniforme sur les varietes drapeaux complètes. Nous nous intéressons au comportement des valeurs propres extrêmes de pi(n)Anpi(n). Il est connu que ce problème est équivalent à l'étude de la mesure de probabilité uniforme sur des polytopes de Gelfand–Tsetlin. Notre résultat principal consiste en des estimées uniformes pour des valeurs propres extrémales, et le fait que les outliers sont de probabilité exponentiellement petite. Ce problème revêt un interêt intrinsèque en matrices aléatoires ; par ailleurs, il trouve une motivation dans des questions d'information quantique que nous évoquons aussi. Les preuves se fonde sur une interpretation du problème a l'aide de processus de points déterminantaux, et les techniques reposent sur de l'analyse de type « steepest descent »

    How to estimate a cumulative process’s rate-function

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    Consider two sequences of bounded random variables, a value and a timing process, that satisfy the large deviation principle (LDP) with rate-function J(·,·) and whose cumulative process satisfies the LDP with rate-function I(·). Under mixing conditions, an LDP for estimates of I constructed by transforming an estimate of J is proved. For the case of cumulative renewal processes it is demonstrated that this approach is favorable to a more direct method as it ensures the laws of the estimates converge weakly to a Dirac measure at I

    How to estimate a cumulative process’s rate-function

    Get PDF
    Consider two sequences of bounded random variables, a value and a timing process, that satisfy the large deviation principle (LDP) with rate-function J(·,·) and whose cumulative process satisfies the LDP with rate-function I(·). Under mixing conditions, an LDP for estimates of I constructed by transforming an estimate of J is proved. For the case of cumulative renewal processes it is demonstrated that this approach is favorable to a more direct method as it ensures the laws of the estimates converge weakly to a Dirac measure at I

    The implications of lung-regulated buoyancy control for dive depth and duration

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    Among air-breathing divers, control of buoyancy through lung volume regulation may be most highly developed in marine turtles. In short, the turtle lung may serve a dual role as both an oxygen store and in buoyancy control. A simple model is developed to show that, for turtles diving up to the maximum depth at which they can still use their lungs to attain neutral buoyancy, the total oxygen store will increase greatly with dive depth, and hence a corresponding increase in dive duration is predicted. Time–depth recorders attached to free-living green turtles (Chelonia mydas) at Ascension Island confirmed a marked increase in dive duration with depth, with the gradient of this relationship being >10 times that seen in diving birds and mammals. Consistent with the prediction that the lungs serve a dual role, we found that, when lead weights were added to some turtles to increase their specific gravity, the mean depth of dives decreased, but for dives to the same depth, weighted animals dived for longer. The depth distribution of green turtles seems to be generally constrained by the maximum depth at which they can still attain close to neutral buoyancy

    Spatial and temporal changes in Bax subcellular localization during anoikis

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    Bax, a member of the Bcl-2 family, translocates to mitochondria during apoptosis, where it forms oligomers which are thought to release apoptogenic factors such as cytochrome c. Using anoikis as a model system, we have examined spatial and temporal changes in Bax distribution. Bax translocates to mitochondria within 15 min of detaching cells from extracellular matrix, but mitochondrial permeabilization does not occur for a number of hours. The formation of Bax oligomers and perimitochondrial clusters occurs concomitant with caspase activation and loss of mitochondrial membrane potential, before nuclear condensation. Cells can be rescued from apoptosis if they are replated onto extracellular matrix within an hour, whereas cells detached for longer could not. The loss of ability to rescue cells from anoikis occurs after Bax translocation, but before the formation of clusters and cytochrome c release. Our data suggest that Bax regulation occurs at several levels, with formation of clusters a late event, and with critical changes determining cell fate occurring earlier
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