On the Diaconis-Shahshahani Method in Random Matrix Theory
نویسندگان
چکیده
منابع مشابه
On the Diaconis-Shahshahani Method in Random Matrix Theory
If is a random variable with values in a compact matrix group K , then the traces Tr( j ) ( j ∈ N) are real or complex valued random variables. As a crucial step in their approach to random matrix eigenvalues, Diaconis and Shahshahani computed the joint moments of any fixed number of these traces if is distributed according to Haar measure and if K is one of Un, On or Spn , where n is large eno...
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Abstract Chung, Diaconis, and Graham considered random processes of the form Xn+1 = 2Xn + bn (mod p) where X0 = 0, p is odd, and bn for n = 0, 1, 2, . . . are i.i.d. random variables on {−1, 0, 1}. If Pr(bn = −1) = Pr(bn = 1) = β and Pr(bn = 0) = 1− 2β, they asked which value of β makes Xn get close to uniformly distributed on the integers mod p the slowest. In this paper, we extend the results...
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3 Universality 4 3.1 Macroscopic behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1.1 Wigner’s semicircle law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Microscopic behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2.1 Bulk universality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2005
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-005-4629-x