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• W2026369120 abstract "We study the statistics of near-extreme events of Brownian motion (BM) on the time interval $[0,t]$. We focus on the density of states near the maximum, $ensuremath{rho}(r,t)$, which is the amount of time spent by the process at a distance $r$ from the maximum. We develop a path integral approach to study functionals of the maximum of BM, which allows us to study the full probability density function of $ensuremath{rho}(r,t)$ and obtain an explicit expression for the moments $⟨[ensuremath{rho}(r,t){]}^{k}⟩$ for arbitrary integer $k$. We also study near extremes of constrained BM, like the Brownian bridge. Finally we also present numerical simulations to check our analytical results." @default.
• W2026369120 created "2016-06-24" @default.
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• W2026369120 date "2013-12-09" @default.
• W2026369120 modified "2023-10-15" @default.
• W2026369120 title "Near-Extreme Statistics of Brownian Motion" @default.
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• W2026369120 doi "https://doi.org/10.1103/physrevlett.111.240601" @default.
• W2026369120 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/24483638" @default.
• W2026369120 hasPublicationYear "2013" @default.
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