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The asymptotics a Bessel-kernel determinant which arises in Random Matrix Theory
In Random Matrix Theory the local correlations of the Laguerre and Jacobi
Unitary Ensemble in the hard edge scaling limit can be described in terms of
the Bessel kernel (containing a parameter ). In particular, the
so-called hard edge gap probabilities can be expressed as the Fredholm
determinants of the corresponding integral operator restricted to the finite
interval [0, R]. Using operator theoretic methods we are going to compute their
asymptotics as R goes to infinity under certain assumption on the parameter
.Comment: 50 page
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