Work

Remarks on Limit Theorems for the Free Quadratic Forms

Year: 2024

Type: article

Abstract: In 2021, Ejsmont and Biernacki showed that the free tangent distribution can be used to measure household satisfaction with durable consumer goods. This distribution arises as the limit of free random variables. This, new article serves as the theoretical introduction to the continuation of the research presented in the paper from 2021. We continue the study of the limit of specific quadratic forms in free probability, which is the first step towards constructing a new distribution for the evaluation of satisfaction with material affluence among household. We formulate a non-central limit theorem for weighted sums of commutators and square of the sums for free random variable. In addition we give the random matrix models for these limits.

Source: Entropy

DOI: 10.3390/e26100870

Authors: Wiktor Ejsmont, Marek Biernacki, Patrycja Hęćka

Institutions: Wrocław University of Science and Technology, Wroclaw University of Economics and Business

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funder: Narodowe Centrum Nauki