On boundary confinements for the Coulomb gas
(2020) In Analysis and Mathematical Physics 10(4).- Abstract
We introduce a family of boundary confinements for Coulomb gas ensembles, and study them in the two-dimensional determinantal case of random normal matrices. The family interpolates between the free boundary and hard edge cases, which have been well studied in various random matrix theories. The confinement can also be relaxed beyond the free boundary to produce ensembles with fuzzier boundaries, i.e., where the particles are more and more likely to be found outside of the boundary. The resulting ensembles are investigated with respect to scaling limits and distribution of the maximum modulus. In particular, we prove existence of a new point field—a limit of scaling limits to the ultraweak point when the droplet ceases to be well... (More)
We introduce a family of boundary confinements for Coulomb gas ensembles, and study them in the two-dimensional determinantal case of random normal matrices. The family interpolates between the free boundary and hard edge cases, which have been well studied in various random matrix theories. The confinement can also be relaxed beyond the free boundary to produce ensembles with fuzzier boundaries, i.e., where the particles are more and more likely to be found outside of the boundary. The resulting ensembles are investigated with respect to scaling limits and distribution of the maximum modulus. In particular, we prove existence of a new point field—a limit of scaling limits to the ultraweak point when the droplet ceases to be well defined.
(Less)
- author
- Ameur, Yacin LU ; Kang, Nam Gyu and Seo, Seong Mi LU
- organization
- publishing date
- 2020
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Hard edge, Planar orthogonal polynomials, Random normal matrices, Scaling limits, Soft edge, Universality
- in
- Analysis and Mathematical Physics
- volume
- 10
- issue
- 4
- article number
- 68
- publisher
- Springer
- external identifiers
-
- scopus:85094673670
- ISSN
- 1664-2368
- DOI
- 10.1007/s13324-020-00406-y
- language
- English
- LU publication?
- yes
- id
- f2970752-d170-416a-8635-08006896702d
- date added to LUP
- 2020-11-13 08:35:12
- date last changed
- 2022-04-26 21:49:18
@article{f2970752-d170-416a-8635-08006896702d, abstract = {{<p>We introduce a family of boundary confinements for Coulomb gas ensembles, and study them in the two-dimensional determinantal case of random normal matrices. The family interpolates between the free boundary and hard edge cases, which have been well studied in various random matrix theories. The confinement can also be relaxed beyond the free boundary to produce ensembles with fuzzier boundaries, i.e., where the particles are more and more likely to be found outside of the boundary. The resulting ensembles are investigated with respect to scaling limits and distribution of the maximum modulus. In particular, we prove existence of a new point field—a limit of scaling limits to the ultraweak point when the droplet ceases to be well defined.</p>}}, author = {{Ameur, Yacin and Kang, Nam Gyu and Seo, Seong Mi}}, issn = {{1664-2368}}, keywords = {{Hard edge; Planar orthogonal polynomials; Random normal matrices; Scaling limits; Soft edge; Universality}}, language = {{eng}}, number = {{4}}, publisher = {{Springer}}, series = {{Analysis and Mathematical Physics}}, title = {{On boundary confinements for the Coulomb gas}}, url = {{http://dx.doi.org/10.1007/s13324-020-00406-y}}, doi = {{10.1007/s13324-020-00406-y}}, volume = {{10}}, year = {{2020}}, }