Identifying Complexity by Means of Matrices
arXiv:cond-mat/0112271 · doi:10.1016/S0378-4371(02)01066-X
Abstract
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related characteristics. Based on several natural complex dynamical systems, like the strongly interacting quantum many-body systems, the human brain and the financial markets, by relating empirical observations to the random matrix theory and quantifying deviations in term of a reduced dimensionality, we present arguments in favour of the statement that complexity is a pheomenon at the edge between collectivity and chaos.
Talk given by S. Drozdz at "Horizons in Complex Systems", Messina, December 5-8, 2001