Войти
Логин:
Пароль:
Забыли пароль?
научная деятельность
структура институтаобразовательные проектыпериодические изданиясотрудники институтапресс-центрконтакты
русский | english

On statistics of bi-orthogonal eigenvectors in non-selfadjoint Gaussian random matrices

 

 Семинар Добрушинской математической лаборатории ИППИ РАН

27 августа, вторник, 16:00, ауд. 307.

Yan Fyodorov (King"s College London):
On statistics of bi-orthogonal eigenvectors in non-selfadjoint Gaussian 
random matrices

Abstract:
I will discuss a method of studying the joint probability density (JPD) of
an eigenvalue and the associated "non-orthogonality overlap factor" (also
known as the "eigenvalue condition number") of the left and right
eigenvectors for non-selfadjoint Gaussian random matrices of size N x N.
I will first derive the general finite N expression for the JPD of a real
eigenvalue and the associated non-orthogonality factor in the real Ginibre
ensemble, and then analyze its "bulk" and "edge" scaling limits. I will
also discuss ongoing work on real elliptic ensembles.
The ensuing distribution is maximally heavy-tailed, so that all integer
moments beyond normalization are divergent. A similar calculation for the
associated non-orthogonality factor in the complex Ginibre ensemble yields
a distribution with the finite first moment complementing recent studies
by P. Bourgade and G. Doubach. Its "bulk" scaling limit yields a
distribution whose first moment reproduces the well-known result of
Chalker and Mehlig (1998), and I will provide the "edge" scaling
distribution for this case as well.
The presentation will be mainly based on the paper:
Y.V. Fyodorov, Commun. Math. Phys. 363 (2), 579-603 (2018)

   Архив прошедших семинаров Добрушинской лаборатории

24.08.2019 | Комеч Сергей Александрович
 

 

  © Федеральное государственное бюджетное учреждение науки
Институт проблем передачи информации им. А.А. Харкевича Российской академии наук, 2019
Об институте  |  Контакты  |  Старая версия сайта