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- W3099692350 abstract "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 $$Wtimes W$$ random Gaussian blocks (parametrized by $$j,k in Lambda =[1,n]^dcap mathbb {Z}^d$$ ) 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 $$Wrightarrow infty $$ 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 $$beta , nrightarrow infty $$ , 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." @default.
- W3099692350 created "2020-11-23" @default.
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- W3099692350 date "2018-02-01" @default.
- W3099692350 modified "2023-10-17" @default.
- W3099692350 title "Universality for 1d Random Band Matrices: Sigma-Model Approximation" @default.
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- W3099692350 doi "https://doi.org/10.1007/s10955-018-1969-1" @default.
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