منابع مشابه
Global fluctuations and Gumbel statistics.
We explain how the statistics of global observables in correlated systems can be related to extreme value problems and to Gumbel statistics. This relationship then naturally leads to the emergence of the generalized Gumbel distribution Ga(x), with a real index a, in the study of global fluctuations. To illustrate these findings, we introduce an exactly solvable nonequilibrium model describing a...
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We study the global fluctuations for linear statistics of the form ∑ n i=1 f(λi) as n → ∞, for C functions f , and λ1, . . . , λn being the eigenvalues of a (general) β-Jacobi ensemble [18, 29]. The fluctuation from the mean ( ∑ n i=1 f(λi)− E ∑ n i=1 f(λi)) is given asymptotically by a Gaussian process. We compute the covariance matrix for the process and show that it is diagonalized by a shif...
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We study analytically the distribution of the minimum of a set of hierarchically correlated random variables E1, E2,ellipsis, E(N) where E(i) represents the energy of the ith path of a directed polymer on a Cayley tree. If the variables were uncorrelated, the minimum energy would have an asymptotic Gumbel distribution. We show that due to the hierarchical correlations, the forward tail of the d...
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We describe and discuss the application of Gumbel statistics, which model extreme events, to WMAP 5-year measurements of the cosmic microwave background. We find that temperature extrema of the CMB are well modelled by the Gumbel formalism and describe tests for Gaussianity that the approach can provide. Comparison to simulations reveals Gumbel statistics to have only weak discriminatory power ...
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BACKGROUND The spatial and space-time scan statistics are commonly applied for the detection of geographical disease clusters. Monte Carlo hypothesis testing is typically used to test whether the geographical clusters are statistically significant as there is no known way to calculate the null distribution analytically. In Monte Carlo hypothesis testing, simulated random data are generated mult...
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ژورنال
عنوان ژورنال: Physical Review Letters
سال: 2005
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.95.170601