Abstract
Free probability theory is a mathematical generlization of classical probability theory. For free central limit theorem we get the semicircle law as the limit law. E P Wigner came across this probability distribution while studying random matrices.
Similar content being viewed by others
Suggested Reading
E P Wigner, Characteristic vectors of bordered matrices with infinite dimensions, Annals of Math., Vol.62, pp.548–564, 1955.
S Ramasubramanian, The Normal Distribution, From Binomial to Normal, Resonance, Vol.2, No.6, pp.15–24, 1997.
S Ramasubramanian, The Normal Distribution, Some Roles of Normality, Resonance, Vol.2, No.7, pp.27–37, 1997.
K L Chung, Elementary Probability Theory and Stochastic Processes, Narosa Publishing House, New Delhi, 1978.
B V Rajarama Bhat, Operators as Random Variables, in Proceedings of the UGC sponsored national seminar on spectral theory of operators and wavelet analysis, NSS College, Ottapalam, pp.45–51, 2006.
F Hiai and D Petz, The Semicircle Law, Free Random Variables and Entropy, Amer. Math. Society. Mathematical Surveys and Monographs, Vol.77, 2000.
D V Voiculescu, K J Dykema, and A Nica, Free Random variables, Amer. Math. Society, CRM Monograph Series, Vol.1, 1992.
A Nica and R Speicher, Lectures on the Combinatorics of Free Probability, London Math. Soc. Lecture Notes Series, Vol.335, 2006.
N Muraki, The five independences as natural products. Infinite Dimensional Analysis and Quantum Probability, Vol.6, pp.337–371, 2003.
Author information
Authors and Affiliations
Corresponding author
Additional information
B V Rajarama Bhat is a professor of mathematics at the Bangalore Centre of the Indian Statistical Institute. He specializes in quantum probability and operator algebras. He loves nature and wants to plant as many trees as possible.
Rights and permissions
About this article
Cite this article
Rajarama Bhat, B.V. Wigner’s semicircle law and free independence. Reson 14, 970–977 (2009). https://doi.org/10.1007/s12045-009-0093-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12045-009-0093-6