Asymptotic Laws for the Spatial Distribution and the Number of Connected Components of Zero Sets of Gaussian Random Functions
DOI:
https://doi.org/10.15407/mag12.03.205Ключові слова:
гладкі гаусiвські випадкові функцiї кiлькох дiйсних змiнних, число компонент зв'язностi нульової множини, ергодичністьАнотація
Вивчено асимптотичнi закони для числа i просторового розподiлу компонент зв'язностi нульових множин гладких гаусiвських випадкових функцiй кiлькох дiйсних змiнних. Основними прикладами є рiзнi гаусiвськi ансамблi дiйсних полiномiв (алгебраїчних i тригонометричних) високого степеня на сферi i на торi, а також трансляцiйно-iнварiантнi гладкi гаусiвськi випадковi функцiї в евклiдовому просторi, що звуженi на великi областi.
Mathematical Subject Classification: 60G15.
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