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- W2048902248 abstract "In this paper we establish one-dimensional Brownian gas models for the extreme-value laws of Gumbel, Weibull, and Frechet. A gas model is a countable collection of independent particles governed by common diffusion dynamics. The extreme-value laws are the universal probability distributions governing the affine scaling limits of the maxima and minima of ensembles of independent and identically distributed one-dimensional random variables. Using the recently introduced concept of stationary Poissonian intensities, we construct two gas models whose global statistical structures are stationary, and yield the extreme-value laws: a linear Brownian motion gas model for the Gumbel law, and a geometric Brownian motion gas model for the Weibull and Frechet laws. The stochastic dynamics of these gas models are studied in detail, and closed-form analytical descriptions of their temporal correlation structures, their topological phase transitions, and their intrinsic first-passage-time fluxes are presented." @default.
- W2048902248 created "2016-06-24" @default.
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- W2048902248 date "2013-02-12" @default.
- W2048902248 modified "2023-09-27" @default.
- W2048902248 title "Brownian gas models for extreme-value laws" @default.
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- W2048902248 doi "https://doi.org/10.1088/1751-8113/46/9/095003" @default.
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