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The Henslow Fellow Lectures - Use of random matrices

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The second of two half-hour lectures by the Society's Henslow Fellows

Random matrices (matrices with entries that are random) were first introduced in order to solve real physical systems. It all started in the 1950s with Eugene Wigner in nuclear physics. He was studying the energy of nuclei of some particles. The energy of these nuclei can take different values and are solutions to a physical equation involving an Hamiltonian, which in essence contains the characteristics of the physical system (think of it as a matrix of infinite size). But this Hamiltonian is often unknown, so it was not easy to obtain properties about those energies. How are they distributed, for instance? The solution to the problem was to create a finite matrix whose structure captures the essence of the physical system. This made it possible to study the system and find out about the structure of those energies. In our talk we will explain how we can find properties about those energies from this matrix representation, and ask, what is the chance of finding no energy at all in a large interval?

This talk is part of the Cambridge Philosophical Society series.

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