The Local Limit Theorem for Products of Random Matrices

2016 ◽  
pp. 273-285
Author(s):  
Yves Benoist ◽  
Jean-François Quint
Keyword(s):  
Limit Theorem ◽  
Random Matrices ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Products Of Random Matrices

scholarly journals A Local Limit Theorem and Delocalization of Eigenvectors for Polynomials in Two Matrices

2020 ◽  
Author(s):  
Ching-Wei Ho
Keyword(s):  
Limit Theorem ◽  
Random Matrices ◽  
Regularity Condition ◽  
Free Probability ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Boundary Regularity ◽  
Haar Unitary

Abstract We propose a boundary regularity condition for the $M_n({\mathbb{C}})$-valued subordination functions in free probability to prove a local limit theorem and delocalization of eigenvectors for self-adjoint polynomials in two random matrices. We prove this through estimating the pair of $M_n({\mathbb{C}})$-valued approximate subordination functions for the sum of two $M_n({\mathbb{C}})$-valued random matrices $\gamma _1\otimes C_N+\gamma _2\otimes U_N^*D_NU_N$, where $C_N$, $D_N$ are deterministic diagonal matrices, and $U_N$ is Haar unitary.

scholarly journals Central and Local Limit Theorems for Numbers of the Tribonacci Triangle

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 880
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Limit Theorems ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Constructive Proof ◽  
The Central Limit Theorem ◽  
Local Limit Theorems

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

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