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  1. Probability Theory and Related Fields
  2. Probability Theory and Related Fields : Volume 157
  3. Probability Theory and Related Fields : Volume 157, Issue 3-4, December 2013
  4. On fluctuations of Riemann’s zeta zeros
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Probability Theory and Related Fields : Volume 165
Probability Theory and Related Fields : Volume 164
Probability Theory and Related Fields : Volume 163
Probability Theory and Related Fields : Volume 162
Probability Theory and Related Fields : Volume 161
Probability Theory and Related Fields : Volume 160
Probability Theory and Related Fields : Volume 159
Probability Theory and Related Fields : Volume 158
Probability Theory and Related Fields : Volume 157
Probability Theory and Related Fields : Volume 157, Issue 3-4, December 2013
Slow movement of a random walk on the range of a random walk in the presence of an external field
The extremal process of branching Brownian motion
On fluctuations of Riemann’s zeta zeros
Local behavior and hitting probabilities of the $$\text{ Airy}_1$$ process
Gumbel fluctuations for cover times in the discrete torus
Power law Pólya’s urn and fractional Brownian motion
Macroscopic energy diffusion for a chain of anharmonic oscillators
Generators of some non-commutative stochastic processes
A simple method for finite range decomposition of quadratic forms and Gaussian fields
The stable trees are nested
Localization and delocalization of eigenvectors for heavy-tailed random matrices
Metastability in the dilute Ising model
Erratum to: Rough Burgers-like equations with multiplicative noise
Probability Theory and Related Fields : Volume 157, Issue 1-2, October 2013
Probability Theory and Related Fields : Volume 156
Probability Theory and Related Fields : Volume 155
Probability Theory and Related Fields : Volume 154
Probability Theory and Related Fields : Volume 153
Probability Theory and Related Fields : Volume 152
Probability Theory and Related Fields : Volume 151
Probability Theory and Related Fields : Volume 150
Probability Theory and Related Fields : Volume 149
Probability Theory and Related Fields : Volume 148
Probability Theory and Related Fields : Volume 147
Probability Theory and Related Fields : Volume 146
Probability Theory and Related Fields : Volume 145
Probability Theory and Related Fields : Volume 144
Probability Theory and Related Fields : Volume 143
Probability Theory and Related Fields : Volume 142
Probability Theory and Related Fields : Volume 141
Probability Theory and Related Fields : Volume 140
Probability Theory and Related Fields : Volume 139
Probability Theory and Related Fields : Volume 138
Probability Theory and Related Fields : Volume 137
Probability Theory and Related Fields : Volume 136
Probability Theory and Related Fields : Volume 135
Probability Theory and Related Fields : Volume 134
Probability Theory and Related Fields : Volume 133
Probability Theory and Related Fields : Volume 132
Probability Theory and Related Fields : Volume 131
Probability Theory and Related Fields : Volume 130
Probability Theory and Related Fields : Volume 129
Probability Theory and Related Fields : Volume 128
Probability Theory and Related Fields : Volume 127
Probability Theory and Related Fields : Volume 126
Probability Theory and Related Fields : Volume 125
Probability Theory and Related Fields : Volume 124
Probability Theory and Related Fields : Volume 123
Probability Theory and Related Fields : Volume 122
Probability Theory and Related Fields : Volume 121
Probability Theory and Related Fields : Volume 120
Probability Theory and Related Fields : Volume 119
Probability Theory and Related Fields : Volume 118
Probability Theory and Related Fields : Volume 117
Probability Theory and Related Fields : Volume 116
Probability Theory and Related Fields : Volume 115
Probability Theory and Related Fields : Volume 114
Probability Theory and Related Fields : Volume 113
Probability Theory and Related Fields : Volume 112
Probability Theory and Related Fields : Volume 111
Probability Theory and Related Fields : Volume 110
Probability Theory and Related Fields : Volume 109
Probability Theory and Related Fields : Volume 108
Probability Theory and Related Fields : Volume 107

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On fluctuations of Riemann’s zeta zeros

Content Provider Springer Nature Link
Author Kargin, V.
Copyright Year 2012
Abstract It is shown that the normalized fluctuations of Riemann’s zeta zeros around their predicted locations follow the Gaussian law. It is also shown that fluctuations of two zeros, $$\gamma _{k}$$ and $$\gamma _{k+x},$$ with $$x\sim \left( \log k\right) ^{\beta }, \beta >0,$$ for large $$k$$ follow the two-variate Gaussian distribution with correlation $$\left( 1-\beta \right) _{+}\! .$$
Ending Page 604
Page Count 30
Starting Page 575
File Format PDF
ISSN 01788051
e-ISSN 14322064
Journal Probability Theory and Related Fields
Issue Number 3
Volume Number 157
Language English
Publisher Springer Berlin Heidelberg
Publisher Date 2012-11-18
Publisher Place Berlin/Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Random matrices Mathematical and Computational Biology Statistics for Business/Economics/Mathematical Finance/Insurance Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses Theoretical, Mathematical and Computational Physics Operations Research/Decision Theory Probability Theory and Stochastic Processes Relations with random matrices Quantitative Finance
Content Type Text
Resource Type Article
Subject Statistics and Probability Analysis Statistics, Probability and Uncertainty
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