Partial linear eigenvalue statistics for non-Hermitian random matrices

نویسندگان

چکیده

Для случайных $(n\times n)$-матриц $X_n$ с независимыми элементами и собственными значениями $\lambda_1,\ldots,\lambda_n$ в основополагающей работе Б. Райдера Дж. Сильверстейна 2006 г. утверждается, что флуктуации линейных статистик собственных значений $\sum_{i=1}^n f(\lambda_i)$ для достаточно "хороших" тестовых функций $f$ сходятся к гауссовскому распределению. Мы изучаем сумм $\sum_{i=1}^{n-K} f(\lambda_i)$, из которых исключены $K$ выбранных случайным образом значений. В этом случае мы находим предельное распределение показываем, оно не обязано быть гауссовским. Наши результаты справедливы случае, когда фиксировано, стремится бесконечности ростом $n$. доказательстве используются классические положения значений, введенные Э. Мекс М. Мексом 2015 Как следствие наших методов, получаем скорость сходимости эмпирического спектрального распределения матриц круговому закону смысле расстояния Вассерштейна, может представлять самостоятельный интерес.

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ژورنال

عنوان ژورنال: ?????? ???????????? ? ?? ??????????

سال: 2022

ISSN: ['0040-361X', '2305-3151']

DOI: https://doi.org/10.4213/tvp5462