We study the determinant , of the integrable Fredholm operator K (s) acting on the interval (-1, 1) with kernel . This determinant arises in the analysis of a log-gas of interacting particles in the bulk-scaling limit, at inverse temperature , in the presence of an external potential supported on an interval of length . We evaluate, in particular, the double scaling limit of as and , in the region , for any fixed . This problem was first considered by Dyson (Chen Ning Yang: A Great Physicist of the Twentieth Century. International Press, Cambridge, pp. 131-146, 1995).

On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential I / Bothner, Thomas; Deift, Percy; Its, Alexander; Krasovsky, Igor. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 337:3(2015), pp. 1397-1463. [10.1007/s00220-015-2357-1]

On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential I

Bothner, Thomas
;
Its, Alexander;Krasovsky, Igor
2015-01-01

Abstract

We study the determinant , of the integrable Fredholm operator K (s) acting on the interval (-1, 1) with kernel . This determinant arises in the analysis of a log-gas of interacting particles in the bulk-scaling limit, at inverse temperature , in the presence of an external potential supported on an interval of length . We evaluate, in particular, the double scaling limit of as and , in the region , for any fixed . This problem was first considered by Dyson (Chen Ning Yang: A Great Physicist of the Twentieth Century. International Press, Cambridge, pp. 131-146, 1995).
2015
337
3
1397
1463
https://arxiv.org/abs/1407.2910
Bothner, Thomas; Deift, Percy; Its, Alexander; Krasovsky, Igor
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/139110
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