Alexander Its (Brunel & Imperial; on leave from Purdue): 

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Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump. (ES)

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ABSTRACT: 

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We evaluate the large n  asymptotics for the
nxn Hankel determinant whose symbol is the Gaussian
multiplied by a step-like function. We use the Riemann-Hilbert
analysis of orthogonal polynomials to obtain the result.
In addition, we calculate  explicitly the  constant phase
shift in the Chen-Pruessner formula for the related
recurrence coefficients. This is the joint work with I.Krasovsky.

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The reported work is a part  (a case study, in fact)
of a bigger research programme on the asymptotic analysis,
via the Riemann-Hilbert method, of Toeplitz and Hankel determinants
with singular symbols. If the time permits, some other recent results
obtained in the field,  as well as its open questions will be outlined.