title: ÐÑÐ¸Ð¼Ð¿ÑÐ¾ÑÐ¸ÑÐµÑÐºÐ¾Ðµ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ ÑÐ¾Ð±ÑÑÐ²ÐµÐ½Ð½ÑÑ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ð¹ Ð­ÑÐ¼Ð¸ÑÐ¾Ð²ÑÑ Ð°ÑÐ¸Ð¼Ð¼ÐµÑÑÐ¸ÑÐ½Ð¾ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½ÑÑ Ð°Ð½ÑÐ°Ð¼Ð±Ð»ÐµÐ¹ ÑÐ»ÑÑÐ°Ð¹Ð½ÑÑ Ð¼Ð°ÑÑÐ¸Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Asymptotic distribution of eigenvalues of asymmetrically distributed Hermitian random matrices
Creators: name: ÐÐ¾Ð»Ð³Ð¸Ð¹, ÐÐ¸ÐºÑÐ¾Ñ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: ÑÐ»ÑÑÐ°Ð¹Ð½ÑÐµ Ð¼Ð°ÑÑÐ¸ÑÑ
Ð³Ð°ÑÑÑÐ¾Ð²ÑÐºÐ¸Ðµ Ð°Ð½ÑÐ°Ð¼Ð±Ð»Ð¸
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Ð¿Ð¾Ð»Ð¸Ð½Ð¾Ð¼Ñ Ð­ÑÐ¼Ð¸ÑÐ°
Ð¿Ð¾Ð»Ð¸Ð½Ð¾Ð¼Ñ ÐÐ°Ð³ÐµÑÑÐ°
Ð³Ð°ÑÑÑÐ¾Ð²ÑÐºÐ¸Ð¹ ÑÐ½Ð¸ÑÐ°ÑÐ½ÑÐ¹ Ð°Ð½ÑÐ°Ð¼Ð±Ð»Ñ
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Ð³Ð°ÑÑÑÐ¾Ð²ÑÐºÐ¸Ð¹ ÑÐ¸Ð¼Ð¿Ð»ÐµÐºÑÐ¸ÑÐµÑÐºÐ¸Ð¹ Ð°Ð½ÑÐ°Ð¼Ð±Ð»Ñ
Ð°ÑÐ¸Ð¼Ð¼ÐµÑÑÐ¸ÑÐ½ÑÐµ ÑÑÐ¼Ð¸ÑÐ¾Ð²Ñ Ð¼Ð°ÑÑÐ¸ÑÑ
Ð°Ð½ÑÐ°Ð¼Ð±Ð»Ñ ÐÐ¸Ð½Ð¸Ð±ÑÐ°
random matrices
Gaussian ensembles
Wigner semicircle law
Hermite polynomials
Laguerre polynomials
Gaussian Unitary Ensemble
Gaussian Orthogonal Ensemble
Gaussian Symplectic Ensemble
asymmetric Hermitian matrices
Ginibre ensemble

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description: The aim of this work is to study the distribution of eigenvalues in various ensembles of random matrices based on numerical and theoretical methods of analysis. Main research tasks: 1. Investigation of the theoretical foundations of the theory of random matrices, including Gaussian ensembles (GUE, GOE, GSE) and asymmetric Hermitian matrices. 2. Study of the Wigner semicircle law and Hermite and Laguerre polynomials, which play an important role in describing correlation functions and state densities. 3. Analysis of the distribution of eigenvalues in Gaussian ensembles using numerical methods and the Wigner semicircle law. 4. Investigation of asymmetric ensembles, including ensembles of real asymmetric matrices and the Ginibre ensemble. 5. Development and implementation of numerical methods for generating random matrices and analyzing the distribution of their eigenvalues. Main results: â¢ Theoretical analysis of the properties of Gaussian ensembles and their influence on the distribution of eigenvalues â¢ Development and implementation of software code for generating random matrices and calculating their eigenvalues. â¢ Conducting numerical experiments confirming theoretical predictions and revealing the influence of ensemble parameters on the distribution of eigenvalues. â¢ Study of the influence of the parameter Î±\alphaÎ± determining the degree of asymmetry of the matrix, and the parameter Î²\betaÎ² related to the Vandermonde module. â¢ Use of logarithmic transformations and multiprocessing to increase the accuracy and efficiency of calculations. â¢ The obtained results can be used for modeling and analyzing complex systems in various fields of science and technology. This work makes a significant contribution to understanding the distribution of eigenvalues in various ensembles of random matrices and proposes effective methods for their numerical analysis.