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    Towards rigorous analysis of the Levitov-Mirlin-Evers recursion 
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    Towards rigorous analysis of the Levitov-Mirlin-Evers recursion

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    Submitted version (480.3Kb)
    Publisher URL
    http://dx.doi.org/10.1088/0951-7715/29/12/3871
    DOI
    10.1088/0951-7715/29/12/3871
    Metadata
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    Abstract
    This paper aims to develop a rigorous asymptotic analysis of an approximate renormalization group recursion for inverse participation ratios $P_q$ of critical powerlaw random band matrices. The recursion goes back to the work by Mirlin and Evers [37] and earlier works by Levitov [32, 33] and is aimed to describe the ensuing multifractality of the eigenvectors of such matrices. We point out both similarities and dissimilarities of LME recursion to those appearing in the theory of multiplicative cascades and branching random walks and show that the methods developed in those fields can be adapted to the present case. In particular the LME recursion is shown to exhibit a phase transition, which we expect is a freezing transition, where the role of temperature is played by the exponent $q$. However, the LME recursion has features that make its rigorous analysis considerably harder and we point out several open problems for further study
    Authors
    Fyodorov, YV; Kupiainen, A; Webb, C
    URI
    http://qmro.qmul.ac.uk/xmlui/handle/123456789/10670
    Collections
    • Particle Physics [828]
    Licence information
    http://arxiv.org/abs/1509.01366
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