#### DMCA

## of a random permutation matrix (2000)

### Citations

522 |
Uniform distribution of sequences
- Kuipers, Niederreiter
- 1974
(Show Context)
Citation Context ...a<b 1 AN([a� b)) ; (b ; a) : N As one would expect, D N (x) ! 0asN !1precisely when x is uniformly distributed. For a proof of this (and other statements in this section) see Kuipers and Niederreiter =-=[5]-=-. We will nd it useful to consider a slightly restricted notion of discrepancy: D N(x) = sup 0<a 1 A N ([0�a)) N ; a : This is equivalent (in the sense that DN DN 2DN ) but has the advantage of having... |

117 | On the distribution of spacings between zeros of the zeta function
- Odlyzko
- 1987
(Show Context)
Citation Context ...s similaritywas rst observed by Montgomery [6] (through conversations with Freeman Dyson in the early 1970's) and has since been supported by various numerical and analytic results (see, for example, =-=[7, 8, 3]-=-). Most of this work has focused on random matrices with continuous distributions, such as Haar measure on the unitary group (the CUE ensemble) or random hermitian matrices with complex iid Gaussian e... |

86 | The pair correlation of zeros of the zeta function
- Montgomery
- 1973
(Show Context)
Citation Context ...arity between eigenvalue distributions of certain random matrices and the distribution of the zeros of the Riemann zeta function along the critical line. This similaritywas rst observed by Montgomery =-=[6]-=- (through conversations with Freeman Dyson in the early 1970's) and has since been supported by various numerical and analytic results (see, for example, [7, 8, 3]). Most of this work has focused on r... |

44 |
Poisson process approximations for the Ewens Sampling Formula
- Arratia, Barbour, et al.
- 1992
(Show Context)
Citation Context ...ppose 2 S n has cycle structure 1 c1 2 c2 :::. Then (t) = Q n j=1 (tj ; 1) cj . Let C j(n) denote the numberofcyclesoflengthj in a random permutation of length n. The Feller coupling, see for example =-=[1]-=-, allows one to construct independent random variables Z j on the same probability space as the C j(n) in such away that Z j is Poisson with mean 1=j, and Ej nX j=1 for any complex sequence aj. a j(Z ... |

39 |
Random matrix theory and the Riemann zeros II; n-point correlations. Nonlinearity 9
- Bogomolny, Keating
- 1996
(Show Context)
Citation Context ...s similaritywas rst observed by Montgomery [6] (through conversations with Freeman Dyson in the early 1970's) and has since been supported by various numerical and analytic results (see, for example, =-=[7, 8, 3]-=-). Most of this work has focused on random matrices with continuous distributions, such as Haar measure on the unitary group (the CUE ensemble) or random hermitian matrices with complex iid Gaussian e... |

34 |
Sets of fractional dimensions IV: On rational approximation to real numbers,
- Besicovitch
- 1934
(Show Context)
Citation Context ...by L = fx 2 RnQ : 8n 2 N� 9q 2 N : kqxk <q ;n g: It is easy to see that if a number is not of nite type, then it is in L. It is a classical result that L is a small set which has Hausdor dimension 0, =-=[2]-=-. For numbers of nite type we have astrongcontrol on their discrepancy. Theorem 2.3. Let have nite type and let xn = fn g. Then for every >0 we have DN (x) =O N ; 1 + . 2.3 Elementary analytic results... |

24 | Developments in random matrix theory,
- Forrester, Snaith, et al.
- 2003
(Show Context)
Citation Context ...in result of this paper is that a similar statement is true for values of the characteristic polynomial. The characteristic polynomial of a random unitary matrix was rst studied by Keating and Snaith =-=[4]-=-. They propose a renormalized version of this random polynomial as a model for the Riemann zeta function along the critical line. They also prove acentral theorem for the value distribution of the pol... |

21 |
Eigenvalue distributions of random permutation matrices
- Wieand
(Show Context)
Citation Context ...rix to look very di erent from that of a random unitary matrix, and indeed it does, 1sbut in many respects it is surprisingly similar. This was rst observed in the PhD thesis of Wieand [10] (see also =-=[11]-=-) where it is shown that the order of the uctuations for the number of eigenvalues in a (nice) subset of the circle is the same as in the unitary case 1 . The main result of this paper is that a simil... |

18 |
Eigenvalue Distributions of Random Matrices in the Permutation Group and Compact Lie Groups
- Wieand
- 1998
(Show Context)
Citation Context ...permutation matrix to look very di erent from that of a random unitary matrix, and indeed it does, 1sbut in many respects it is surprisingly similar. This was rst observed in the PhD thesis of Wieand =-=[10]-=- (see also [11]) where it is shown that the order of the uctuations for the number of eigenvalues in a (nice) subset of the circle is the same as in the unitary case 1 . The main result of this paper ... |

8 |
The n-level correlations of zeros of the zeta function
- Rudnick, Sarnak
- 1994
(Show Context)
Citation Context ...s similaritywas rst observed by Montgomery [6] (through conversations with Freeman Dyson in the early 1970's) and has since been supported by various numerical and analytic results (see, for example, =-=[7, 8, 3]-=-). Most of this work has focused on random matrices with continuous distributions, such as Haar measure on the unitary group (the CUE ensemble) or random hermitian matrices with complex iid Gaussian e... |