Random Normal Matrices : Eigenvalue Correlations Near a Hard Wall
(2024) In Journal of Statistical Physics 191(8).- Abstract
We study pair correlation functions for planar Coulomb systems in the pushed phase, near a ring-shaped impenetrable wall. We assume coupling constant Γ=2 and that the number n of particles is large. We find that the correlation functions decay slowly along the edges of the wall, in a narrow interface stretching a distance of order 1/n from the hard edge. At distances much larger than 1/n, the effect of the hard wall is negligible and pair correlation functions decay very quickly, and in between sits an interpolating interface that we call the “semi-hard edge”. More precisely, we provide asymptotics for the correlation kernel Kn(z,w) as n→∞ in two microscopic regimes (with either |z-w|=O(1/n) or |z-w|=O(1/n)), as well as in... (More)
We study pair correlation functions for planar Coulomb systems in the pushed phase, near a ring-shaped impenetrable wall. We assume coupling constant Γ=2 and that the number n of particles is large. We find that the correlation functions decay slowly along the edges of the wall, in a narrow interface stretching a distance of order 1/n from the hard edge. At distances much larger than 1/n, the effect of the hard wall is negligible and pair correlation functions decay very quickly, and in between sits an interpolating interface that we call the “semi-hard edge”. More precisely, we provide asymptotics for the correlation kernel Kn(z,w) as n→∞ in two microscopic regimes (with either |z-w|=O(1/n) or |z-w|=O(1/n)), as well as in three macroscopic regimes (with |z-w|≍1). For some of these regimes, the asymptotics involve oscillatory theta functions and weighted Szegő kernels.
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- author
- Ameur, Yacin LU ; Charlier, Christophe LU and Cronvall, Joakim LU
- organization
- publishing date
- 2024-08
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- 41A60, 60B20, 60G55, Correlation kernel, Hard wall, Pushed phase, Random normal matrices, Theta functions
- in
- Journal of Statistical Physics
- volume
- 191
- issue
- 8
- article number
- 98
- publisher
- Springer
- external identifiers
-
- scopus:85200910432
- ISSN
- 0022-4715
- DOI
- 10.1007/s10955-024-03314-8
- language
- English
- LU publication?
- yes
- id
- 84b45dca-66ac-4350-9b84-a23fa198412e
- date added to LUP
- 2024-09-10 15:23:14
- date last changed
- 2024-09-10 15:24:06
@article{84b45dca-66ac-4350-9b84-a23fa198412e,
abstract = {{<p>We study pair correlation functions for planar Coulomb systems in the pushed phase, near a ring-shaped impenetrable wall. We assume coupling constant Γ=2 and that the number n of particles is large. We find that the correlation functions decay slowly along the edges of the wall, in a narrow interface stretching a distance of order 1/n from the hard edge. At distances much larger than 1/n, the effect of the hard wall is negligible and pair correlation functions decay very quickly, and in between sits an interpolating interface that we call the “semi-hard edge”. More precisely, we provide asymptotics for the correlation kernel K<sub>n</sub>(z,w) as n→∞ in two microscopic regimes (with either |z-w|=O(1/n) or |z-w|=O(1/n)), as well as in three macroscopic regimes (with |z-w|≍1). For some of these regimes, the asymptotics involve oscillatory theta functions and weighted Szegő kernels.</p>}},
author = {{Ameur, Yacin and Charlier, Christophe and Cronvall, Joakim}},
issn = {{0022-4715}},
keywords = {{41A60; 60B20; 60G55; Correlation kernel; Hard wall; Pushed phase; Random normal matrices; Theta functions}},
language = {{eng}},
number = {{8}},
publisher = {{Springer}},
series = {{Journal of Statistical Physics}},
title = {{Random Normal Matrices : Eigenvalue Correlations Near a Hard Wall}},
url = {{http://dx.doi.org/10.1007/s10955-024-03314-8}},
doi = {{10.1007/s10955-024-03314-8}},
volume = {{191}},
year = {{2024}},
}