scholarly journals Evidence of Random Matrix Corrections for the Large Deviations of Selberg’s Central Limit Theorem

2021 ◽  
pp. 1-13
Author(s):  
E. Amzallag ◽  
L.-P. Arguin ◽  
E. Bailey ◽  
K. Huib ◽  
R. Rao
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Large Deviations ◽  
Central Limit ◽  
Random Matrix

On the behaviour of a long cascade of linear reservoirs

2000 ◽  
Vol 37 (02) ◽  
pp. 417-428
Author(s):  
John E. Glynn ◽  
Peter W. Glynn
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Large Deviations ◽  
Asymptotic Behaviour ◽  
Central Limit ◽  
Tail Probabilities ◽  
Logarithmic Asymptotics ◽  
Random Fluctuations

This paper describes the limiting asymptotic behaviour of a long cascade of linear reservoirs fed by stationary inflows into the first reservoir. We show that the storage in the nth reservoir becomes asymptotically deterministic as n → ∞, and establish a central limit theorem for the random fluctuations about the deterministic approximation. In addition, we prove a large deviations theorem that provides precise logarithmic asymptotics for the tail probabilities associated with the storage in the nth reservoir when n is large.

On the behaviour of a long cascade of linear reservoirs

2000 ◽  
Vol 37 (2) ◽  
pp. 417-428
Author(s):  
John E. Glynn ◽  
Peter W. Glynn
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Large Deviations ◽  
Asymptotic Behaviour ◽  
Central Limit ◽  
Tail Probabilities ◽  
Logarithmic Asymptotics ◽  
Random Fluctuations

This paper describes the limiting asymptotic behaviour of a long cascade of linear reservoirs fed by stationary inflows into the first reservoir. We show that the storage in the nth reservoir becomes asymptotically deterministic as n → ∞, and establish a central limit theorem for the random fluctuations about the deterministic approximation. In addition, we prove a large deviations theorem that provides precise logarithmic asymptotics for the tail probabilities associated with the storage in the nth reservoir when n is large.

scholarly journals A CENTRAL LIMIT THEOREM FOR THE ZEROES OF THE ZETA FUNCTION

2014 ◽  
Vol 10 (02) ◽  
pp. 483-511 ◽  
Author(s):  
BRAD RODGERS
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Zeta Function ◽  
Central Limit ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Riemann Hypothesis ◽  
Matrix Theory ◽  
Riemann’S Zeta Function

On the assumption of the Riemann hypothesis, we generalize a central limit theorem of Fujii regarding the number of zeroes of Riemann's zeta function that lie in a mesoscopic interval. The result mirrors results of Spohn and Soshnikov and others in random matrix theory. In an appendix we put forward some general theorems regarding our knowledge of the zeta zeroes in the mesoscopic regime.

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