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T:A:L:K:S
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title:
Random Matrix Distributions, Operator Determinants, and Numerical Noise |
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name:
Bornemann |
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first name:
Folkmar
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location/conference:
SPP-JT14
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PRESENTATION-link:
http://www.dfg-spp1324.de/nuhagtools/event_NEW/dateien/SPP-JT14/slides/bornemann_fc14.pdf |
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abstract:
Because of universal scaling laws, distributions and correlation functions of classical random matrix ensembles and combinatorial growth processes in the large size limits have become increasingly important in physics and statistics. Their effective numerical computation has been made possible by evaluating higher derivatives of operator determinants. We review the underlying mathematical ideas and demonstrate how numerical explorations have led to new formulae, to new numerical algorithms, and finally allowed to exhibit universal scaling in some concrete physical experiments. Special attention is given to the sharp assessment of numerical errors: we relate them to a robust statistics of numerical noise in the tail of Chebyshev expansions. |
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