Klein, A (California, Irvine)
Tuesday 03 April 2007, 
Quantum Graphs, their Spectra and Applications

Uniform existence of the integrated density of states for random Schrodinger operators on metric graphs over Z$^d$

Analysis on graphs and other discrete structures has been developing for quite some time, in particular due to applications to number theory, algebra, probability theory, spectral geometry, as well as to its usefulness in many practical problems. This area, however, has experienced recently a significant boost in terms of new important applications arising, new methods being developed, and new models introduced not studied before. This has happened due to numerous new applications arising in different areas of mathematics, sciences, and engineering. They swipe throughout a wide scientific landscape, which besides the fields already mentioned includes nanotechnology, microelectronics, quantum chemistry, superconductivity, optics, etc.

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