The paper continues the development of the rigorous supersymmetric transfer matrix approach to the random band matrices started in (J Stat Phys 164:1233–1260, 2016; Commun Math Phys 351:1009–1044, 2017). We consider random Hermitian block band matrices consisting of $W\times W$ random Gaussian blocks (parametrized by $j,k \in\Lambda=[1,n]^d\cap \mathbb{Z}^d$) with a
fixed entry's variance $J_{jk}=\delta_{j,k}W^{-1}+\beta\Delta_{j,k}W^{-2}$, $\beta>0$ in each block. Taking the limit $W\to\infty$ with fixed $n$ and $\beta$, we
derive the sigma-model approximation of the second correlation function similar to Efetov's one.
Then, considering the limit $\beta, n\to\infty$, we prove that in the dimension $d=1$ the behaviour of the sigma-model approximation in the bulk of the spectrum, as $\beta\gg n$, is determined by the classical Wigner -- Dyson statistics.
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Dynamical Localization for Random Band Matrices Up to $$W\ll N^{1/4}$$
We prove that a large class of N × N Gaussian random band matrices with band width W exhibits dynamical Anderson localization at all energies when $$W <
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- NSF-PAR ID:
- 10514696
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Communications in Mathematical Physics
- Volume:
- 405
- Issue:
- 3
- ISSN:
- 0010-3616
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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The paper continues (Shcherbina and Shcherbina in Commun Math Phys 351:1009–1044, 2017); Shcherbina in Commun Math Phys 328:45–82, 2014) which study the behaviour of second correlation function of characteristic polynomials of the special case of $n \times n$ one-dimensional Gaussian Hermitian random band matrices, when the covariance of the elements is determined by the matrix $𝐽=(-W^2\triangle+1)^{-1}$. Applying the transfer matrix approach, we study the case when the bandwidth W is proportional to the threshold $\sqrt{n}$more » « less
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Abstract Survival of Gulf Stream (GS) warm core rings (WCRs) was investigated using a census consisting of a total of 961 rings formed during the period 1980–2017. Kaplan‐Meier survival probability and Cox hazard proportional models were used for the analysis. The survival analysis was performed for rings formed in four 5° zones between 75° W and 55° W. The radius, latitude, and distance from the shelf‐break of a WCR at formation all had a significant effect on the survival of WCRs. A pattern of higher survival was observed in WCRs formed in Zone 2 (70°–65° W) or Zone 3 (65°–60° W) and then demised in Zone 1 (75°–70° W). Survival probability of the WCRs increased to more than
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