Large deviations of Gaussian random functions

<p>A random function – of either one variable (a <a href="/facts/Random_process/Ng1n1dnB">random process</a>), or two or more variables
(a <a href="/facts/Random_field/8N7Id48z">random field</a>) – is called Gaussian if every <a href="/facts/Finite-dimensional_distribution/RRglj3hV">finite-dimensional distribution</a> is a <a href="/facts/Multivariate_normal_distribution/2Xfegqz2">multivariate normal distribution</a>. Gaussian random fields on the <a href="/facts/Sphere/jywYLNM2">sphere</a> are useful (for example) when analysing
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<ul><li>the anomalies in the <a href="/facts/Cosmic_microwave_background_radiation/ThB2HkLS">cosmic microwave background radiation</a> (see, pp. 8–9);</li>
<li>brain images obtained by <a href="/facts/Positron_emission_tomography/5SmcW6qz">positron emission tomography</a> (see, pp. 9–10).</li></ul>
<p>Sometimes, a value of a Gaussian random function deviates from its <a href="/facts/Expected_value/1XV0JKL8">expected value</a> by several <a href="/facts/Standard_deviation/qSug9BRl">standard deviations</a>. This is a large deviation. Though rare in a small domain (of space or/and time), large deviations may be quite usual in a large domain.
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Large deviations of Gaussian random functions open-in-new

Large deviations of Gaussian random functions