1,720,974 research outputs found
Central Spectral Gaps of the Almost Mathieu Operator
Full text linkWe consider the spectrum of the almost Mathieu operator Hα with frequency α
and in the case of the critical coupling. Let an irrational α be such that |α − pn/qn| < cq−κ
n
,
where pn/qn, n = 1, 2, . . . are the convergents to α, and c, κ are positive absolute constants,
κ < 56. Assuming certain conditions on the parity of the coefficients of the continued
fraction of α, we show that the central gaps of Hpn/qn
, n = 1, 2, . . . , are inherited as spectral
gaps of Hα of length at least c
0
q
−κ/2
n , c
0 > 0
Asymptotics of the Airy-Kernel Determinant
No full textThe authors use Riemann-Hilbert methods to compute the constant that arises in the asymptotic behavior of the Airy-kernel determinant of random matrix theory
Sine‐kernel determinant on two large intervals
Full text linkWe consider the probability of two large gaps (intervals without eigenvalues) in the bulk scaling limit of the Gaussian Unitary Ensemble of random matrices. We determine the multiplicative constant in the asymptotics. We also provide the full explicit asymptotics (up to decreasing terms) for the transition between one and two large gaps
On the spectrum of critical almost Mathieu operators in the rational case
Full text linkWe derive a new Chambers-type formula and prove sharper upper bounds on the measure of the spectrum of critical almost Mathieu operators with rational frequencies
Probability of Two Large Gaps in the Bulk and at the Edge of the Spectrum of Random Matrices
No full textWe present the probability of two large gaps (intervals without eigenvalues) in the bulk and also in the edge scaling limit of the Gaussian Unitary Ensemble of random matrices
Weak and Strong Confinement in the Freud Random Matrix Ensemble and Gap Probabilities
Full text linkThe Freud ensemble of random matrices is the unitary invariant ensemble corresponding to the weight exp(-n vertical bar x vertical bar(beta)), beta > 0, on the real line. We consider the local behaviour of eigenvalues near zero, which exhibits a transition in beta. If beta >= 1, it is described by the standard sine process. Below the critical value beta = 1, it is described by a process depending on the value of beta, and we determine the first two terms of the large gap probability in it. This so called weak confinement range 0 < beta < 1 corresponds to the Freud weight with the indeterminate moment problem. We also find the multiplicative constant in the asymptotic expansion of the Freud multiple integral for beta >= 1
Asymptotics for a determinant with a confluent hypergeometric kernel
Full text linkWe obtain "large gap" asymptotics for a Fredholm determinant with a confluent hyper-geometric kernel. We also obtain asymptotics for determinants with two types of Bessel kernels which appeared in random matrix theory
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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