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@article{Bothner:2015:10.1007/s00220-015-2357-1,
author = {Bothner, T and Deift, P and Its, A and Krasovsky, I},
doi = {10.1007/s00220-015-2357-1},
journal = {Communications in Mathematical Physics},
pages = {1397--1463},
title = {On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential I},
url = {http://dx.doi.org/10.1007/s00220-015-2357-1},
volume = {337},
year = {2015}
}

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TY  - JOUR
AB  - We study the determinant det(I−γKs),0<γ<1 , of the integrable Fredholm operator K s acting on the interval (−1, 1) with kernel Ks(λ,μ)=sins(λ−μ)π(λ−μ) . This determinant arises in the analysis of a log-gas of interacting particles in the bulk-scaling limit, at inverse temperature β=2 , in the presence of an external potential v=−12ln(1−γ) supported on an interval of length 2sπ . We evaluate, in particular, the double scaling limit of det(I−γKs) as s→∞ and γ↑1 , in the region 0≤κ=vs=−12sln(1−γ)≤1−δ , for any fixed 0<δ<1 . This problem was first considered by Dyson (Chen Ning Yang: A Great Physicist of the Twentieth Century. International Press, Cambridge, pp. 131–146, 1995).
AU  - Bothner,T
AU  - Deift,P
AU  - Its,A
AU  - Krasovsky,I
DO  - 10.1007/s00220-015-2357-1
EP  - 1463
PY  - 2015///
SN  - 0010-3616
SP  - 1397
TI  - On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential I
T2  - Communications in Mathematical Physics
UR  - http://dx.doi.org/10.1007/s00220-015-2357-1
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000353506500011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://link.springer.com/article/10.1007%2Fs00220-015-2357-1
VL  - 337
ER  -

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