Zobrazeno 1 - 10
of 19
pro vyhledávání: '"11M50, 15B52"'
Autor:
Simm, Nick, Wei, Fei
We consider the derivative of the characteristic polynomial of $N \times N$ Haar distributed unitary matrices. In the limit $N \to \infty$, we give a formula for general non-integer moments of the derivative for values of the spectral variable inside
Externí odkaz:
http://arxiv.org/abs/2409.03687
Autor:
Barrett, Owen, Batterman, Zoë X., Jambhale, Aditya, Miller, Steven J., Narayanan, Akash L., Sharma, Kishan, Yao, Chris
The Katz-Sarnak philosophy states that statistics of zeros of $L$-function families near the central point as the conductors tend to infinity agree with those of eigenvalues of random matrix ensembles as the matrix size tends to infinity. While numer
Externí odkaz:
http://arxiv.org/abs/2407.14526
Autor:
Khorunzhiy, O.
Using recent results on the concentration of the largest eigenvalue and maximal vertex degree of large random graphs, we show that the infinite sequence of Erd\H os-R\'enyi random graphs $G(n,\rho_n/n)$ such that $\rho_n/\log n$ infinitely increases
Externí odkaz:
http://arxiv.org/abs/2101.03338
Autor:
Riedtmann, Helen
We provide a combinatorial derivation of an asymptotic formula for averages of mixed ratios of characteristic polynomials over the unitary group, where mixed ratios are products of ratios and/or logarithmic derivatives. Our proof of this formula is a
Externí odkaz:
http://arxiv.org/abs/1805.07261
Autor:
Riedtmann, Helen
Our results can be viewed as applications of algebraic combinatorics in random matrix theory. These applications are motivated by the predictive power of random matrix theory for the statistical behavior of the celebrated Riemann $\zeta$-function (an
Externí odkaz:
http://arxiv.org/abs/1805.07245
Autor:
Bourgade, Paul, Kuan, Jeffrey
Assuming the Riemann hypothesis, we prove the weak convergence of linear statistics of the zeros of L-functions towards a Gaussian field, with covariance structure corresponding to the $\HH^{1/2}$-norm of the test functions. For this purpose, we obta
Externí odkaz:
http://arxiv.org/abs/1203.5328
Autor:
Dueñez, Eduardo, Farmer, David W., Froehlich, Sara, Hughes, Chris, Mezzadri, Francesco, Phan, Toan
Publikováno v:
Nonlinearity, Vol. 23 (2010), 2599-2621
We investigate the horizontal distribution of zeros of the derivative of the Riemann zeta function and compare this to the radial distribution of zeros of the derivative of the characteristic polynomial of a random unitary matrix. Both cases show a s
Externí odkaz:
http://arxiv.org/abs/1002.0372
We investigate the horizontal distribution of zeros of the derivative of the Riemann zeta function and compare this to the radial distribution of zeros of the derivative of the characteristic polynomial of a random unitary matrix. Both cases show a s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0f3843b0da3c7e5a1b785665b811d5b0
Autor:
Rodgers, Brad
Publikováno v:
Commentarii Mathematici Helvetici; 2017, Vol. 92 Issue 2, p311-347, 37p
Autor:
Mason, A. M., Snaith, N. C.
Publikováno v:
Random Matrices: Theory & Application; Oct2016, Vol. 5 Issue 4, p-1, 36p