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• W2140165772 startingPage "1449" @default.
• W2140165772 abstract "We obtain an asymptotic expansion for the tails of the random variable $tcal=argmax_{uinmathbb{R}}(mathcal{A}_2(u)-u^2)$ where $mathcal{A}_2$ is the Airy$_2$ process. Using the formula of Schehr cite{Sch} that connects the density function of $tcal$ to the Hastings-McLeod solution of the second Painlev'e equation, we prove that as $trightarrowinfty$, $mathbb{P}(|tcal|>t)=Ce^{-4/3varphi(t)}t^{-145/32}(1+O(t^{-3/4}))$, where $varphi(t)=t^3-2t^{3/2}+3t^{3/4}$, and the constant $C$ is given explicitly." @default.
• W2140165772 created "2016-06-24" @default.
• W2140165772 creator A5010479745 @default.
• W2140165772 creator A5056954086 @default.
• W2140165772 date "2013-04-15" @default.
• W2140165772 modified "2023-09-28" @default.
• W2140165772 title "Tail decay for the distribution of the endpoint of a directed polymer" @default.
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• W2140165772 doi "https://doi.org/10.1088/0951-7715/26/5/1449" @default.
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