László Erdős, professor at the Institute of Science and Technology Austria (IST Austria), shares the Erwin Schrödinger Prize of the Austrian Academy of Sciences (ÖAW) with physicist Markus Arndt professor at the University of Vienna.
IST says the Hungarian mathematician is being honored for his outstanding research achievements at the interface between mathematics and physics, particularly for his pioneering work on random matrices.
As the Institite explains, in the 1950s, Hungarian Nobel Prize winner Jenő ('Eugene') Wigner was looking for a mathematical way to describe heavy atomic nuclei. The aim was to find the distribution of their energy levels, the so-called spectrum, because it defines many important properties of the atom’s nucleus. For larger nuclei, the known methods were insufficient to handle the complexity of the task. Wigner assumed that the random matrix was a practicable simplification of the problem.
The entries of a matrix, clustered in rows and columns, compactly summarize the parameters of an atomic nucleus. However, if the nucleus is large, so many interacting factors play a role that a square grid with quasi-random numbers can just as well describe the system adequately. The random matrix proved its usefulness in experiments, but mathematically the procedure remained largely an open quest.
László Erdős and his team took up this challenge and established many fundamental results of random matrices in detail. Their extensions to increasingly complex systems paved the way for the theory’s broad application. Apart from heavy atomic nuclei, random matrices are employed in telecommunications, in the analysis of artificial as well as natural neural networks and in big data statistics.
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