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Creators/Authors contains: "Shcherbina, Tatyana"

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  1. ; (, Journal of Statistical Physics)
    Free, publicly-accessible full text available January 15, 2026
  2. ; (, Zurnal matematiceskoj fiziki, analiza, geometrii)
    Full Text Available 
  3. ; (, Journal of Statistical Physics)
    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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