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            <title xml:lang="en">Anderson transition for Google matrix eigenstates</title>
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                <forename type="first">O. V.</forename>
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            <idno type="halRefHtml">&lt;i&gt;Annalen der Physik&lt;/i&gt;, 2015, 527 (9-10), pp.713. &lt;a target="_blank" href="https://dx.doi.org/10.1002/andp.201500110"&gt;&amp;#x27E8;10.1002/andp.201500110&amp;#x27E9;&lt;/a&gt;</idno>
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                <title xml:lang="en">Anderson transition for Google matrix eigenstates</title>
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                <term xml:lang="en">Markov chains</term>
                <term xml:lang="en">Anderson localization</term>
                <term xml:lang="en">PageRank</term>
                <term xml:lang="en">Google matrix</term>
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              <p>We introduce a number of random matrix models describing the Google matrix G of directed networks. The properties of their spectra and eigenstates are analyzed by numerical matrix diagonalization. We show that for certain models it is possible to have an algebraic decay of PageRank vector with the exponent similar to real directed networks. At the same time the spectrum has no spectral gap and a broad distribution of eigenvalues in the complex plain. The eigenstates of G are characterized by the Anderson transition from localized to delocalized states and a mobility edge curve in the complex plane of eigenvalues.</p>
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