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Strong Log-Concavity of Chernoff's Density

Probability & statistics · posed by Fadoua Balabdaoui & Jon A. Wellner, 2014 · solved

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Statement

Is the density of Chernoff's distribution - the law of argmax⁡t{W(t)−t2}\operatorname{argmax}_t \{W(t) - t^2\} for two-sided Brownian motion WW - strongly log-concave, as conjectured by Balabdaoui and Wellner in 2014?

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    GPT-5.6 Sol, with Xianyang Zhang and Quan Zhou

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    AI involvement
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    The proof was generated in its entirety by GPT-5.6 Sol; the authors checked it and prepared the manuscript.

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