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УМН, 2000, том 55, выпуск 5(335), страницы 107–160 (Mi umn321)  

Эта публикация цитируется в 309 научных статьях (всего в 309 статьях)

Детерминантные случайные точечные поля

А. Б. Сошников

University of California, Berkeley

Аннотация: Статья содержит как хорошо известные, так и новые результаты о детерминантных случайных полях. В первом разделе статьи изложено доказательство теоремы о необходимом и достаточном условии для существования детерминантного случайного поля с эрмитовым ядром и также некоторые смежные технические результаты. Второй раздел посвящен примерам детерминантных случайных полей из квантовой механики, статистической механики, теории случайных матриц, теории вероятностей, теории представлений и эргодической теории. В связи с теорией процессов восстановления мы охарактеризовали все эрмитовы детерминантные случайные поля с независимыми одинаково распределенными спейсингами. В третьем разделе исследуются эргодические свойства трансляционно инвариантных детерминантных случайных точечных полей. В частности, доказываются свойство перемешивания любой кратности и абсолютная непрерывность спектра. В последней секции обсуждается доказательство центральной предельной теоремы для числа частиц в растущем интервале и функциональной центральной предельной теоремы для эмпирической функции распределения спейсингов.
Библиография: 92 названия.

DOI: https://doi.org/10.4213/rm321

Полный текст: PDF файл (546 kB)
Список литературы: PDF файл   HTML файл

Англоязычная версия:
Russian Mathematical Surveys, 2000, 55:5, 923–975

Реферативные базы данных:

УДК: 519.218
MSC: Primary 60G60, 60K35; Secondary 15A52, 60K05, 60F05, 37A25, 82C22
Поступила в редакцию: 11.04.2000

Образец цитирования: А. Б. Сошников, “Детерминантные случайные точечные поля”, УМН, 55:5(335) (2000), 107–160; Russian Math. Surveys, 55:5 (2000), 923–975

Цитирование в формате AMSBIB
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