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    Large deviations in random graphs

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    Date
    2018-05-14
    Author
    Zhao, Yufei
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    Abstract
    What is the probability that the number of triangles in an Erd\H{o}s–R\'enyi random graph exceeds its mean by a constant factor? This problem has been a useful litmus test for concentration bound techniques. Even the order of the log-probability was considered a difficult problem until its resolution a few years ago by Chatterjee and DeMarco--Kahn. I will discuss the problem of determining the exponential rate of the tail probability, and survey some recent developments and open problems.
    URI
    http://hdl.handle.net/1853/59710
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