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A unified approach to fluctuations of LES of time-dependent generalized patterned random matrices
Abstract
A unified approach for studying the linear eigenvalue statistics (LES) of generalized patterned random matrices was developed in Kumar, Maurya, Saha (2026). In this paper, as a continuation, we develop a unified method for studying the time-dependent LES of generalized patterned random matrices with independent process entries such as Brownian motion and Ornstein-Uhlenbeck process. We prove that if the limiting moment sequence of the LES of the generalized patterned random matrix with independent standard Gaussian entries is M-determinate, then under some minimal assumption on the link function, the time-dependent LES converges to a deterministic real-valued process.
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BibTeX
@misc{kumar2026unified,
title = {{A unified approach to fluctuations of LES of time-dependent generalized patterned random matrices}},
author = {Kiran Kumar and Shambhu Nath Maurya and Koushik Saha},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06686},
eprint = {2611.06686},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06686},
}
RIS
TY - UNPB
TI - A unified approach to fluctuations of LES of time-dependent generalized patterned random matrices
AU - Kiran Kumar
AU - Shambhu Nath Maurya
AU - Koushik Saha
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06686
UR - https://arxiv.org/abs/2611.06686
AB - A unified approach for studying the linear eigenvalue statistics (LES) of generalized patterned random matrices was developed in Kumar, Maurya, Saha (2026). In this paper, as a continuation, we develop a unified method for studying the time-dependent LES of generalized patterned random matrices with independent process entries such as Brownian motion and Ornstein-Uhlenbeck process. We prove that if the limiting moment sequence of the LES of the generalized patterned random matrix with independent standard Gaussian entries is M-determinate, then under some minimal assumption on the link function, the time-dependent LES converges to a deterministic real-valued process.
ER -