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            <title xml:lang="af">Random walk on sparse random digraphs</title>
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            <idno type="halRefHtml">&lt;i&gt;Probability Theory and Related Fields&lt;/i&gt;, 2018, 170 (3-4), pp.933-960. &lt;a target="_blank" href="https://dx.doi.org/10.1007/s00440-017-0796-7"&gt;&amp;#x27E8;10.1007/s00440-017-0796-7&amp;#x27E9;&lt;/a&gt;</idno>
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              <p>A finite ergodic Markov chain exhibits cutoff if its distance to equilibrium remains close to its initial value over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Originally discovered in the context of card shuffling (Aldous-Diaconis, 1986), this remarkable phenomenon is now rigorously established for many reversible chains. Here we consider the non-reversible case of random walks on sparse directed graphs, for which even the equilibrium measure is far from being understood. We work under the configuration model, allowing both the in-degrees and the out-degrees to be freely specified. We establish the cutoff phenomenon, determine its precise window and prove that the cutoff profile approaches a universal shape. We also provide a detailed description of the equilibrium measure.</p>
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