Định lý giới hạn trung tâm mesoscopic cho ma trận ngẫu nhiên phi Hermitian

Giorgio Cipolloni1, László Erdős2, Dominik Schröder3
1Princeton Center for Theoretical Science, Princeton University, Princeton, USA
2IST Austria, Klosterneuburg, Austria
3ETH Zurich, Zurich, Switzerland

Tóm tắt

Chúng tôi chứng minh rằng thống kê tuyến tính mesoscopic $$\sum _i f(n^a(\sigma _i-z_0))$$ của các trị riêng $$\{\sigma _i\}_i$$ của các ma trận ngẫu nhiên phi Hermitian lớn có kích thước $$n\times n$$ với các phần tử độc lập và phân phối đồng nhất theo phân phối phức tạp có trung tâm thì có phân phối gần đúng Gaussian asymptotically cho bất kỳ hàm $$H^{2}_0$$ -hàm $$f$$ xung quanh bất kỳ điểm $$z_0$$ nào trong khối của phổ tại bất kỳ thang mesoscopic nào $$0

Từ khóa

#hàm Gaussian #ma trận ngẫu nhiên #lý thuyết giới hạn trung tâm #thống kê tuyến tính #ma trận phi Hermitian

Tài liệu tham khảo

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