4 problems

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Failure of log-convexity for distributions close to the exponential distribution
Failure conjecture. The condition
Conjectureopenexponential-distributions probability-inequalities tail-probabilityarXiv posted 2 days ago
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The polynomial tail lower-bound conjecture for spiral-like domains
Polynomial tail conjecture. For every $p>{\rm H}(W)$ , there exists a constant $C>0$ such that
Conjectureopenexit-times planar-brownian-motion tail-probabilityarXiv posted 2 days ago
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Weighted-average tail conjecture for independent random variables
Let $X$ and $Y$ be independent random variables on $\mathbb{R}_+$ that are not compactly supported, and let $\lambda\in(0,1)$ . Weighted-average tail conjecture. … This conjecture i…
Conjectureopenprobability random-variables tail-probabilityarXiv posted 2 days ago
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The Mieczkowska–Sileikis conjecture for maximal i.i.d. tail probabilities
Let $m_k(x)$ denote the supremum of $\mathbb{P}(X_1+\cdots+X_k\geq 1)$ over nonnegative, independent and identically distributed random variables with $\mathbb{E}(X_i)\leq x$ . For…
Conjectureopenextremal-combinatorics probability tail-probabilityarXiv posted 2 days ago

Failure of log-convexity for distributions close to the exponential distribution