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On boundary confinements for the Coulomb gas

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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 defined.

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Funding

Nam-Gyu Kang was partially supported by Samsung Science and Technology Foundation (SSTF-BA1401-51) and by a KIAS Individual Grant (MG058103) at Korea Institute for Advanced Study.

Seong-Mi Seo was partially supported by a KIAS Individual Grant (MG063103) at Korea Institute for Advanced Study and by a National Research Foundation of Korea Grant funded by the Korea government (No. 2019R1F1A1058006).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Lund University, P.O. BOX 118, 221 00, Lund, Sweden

    Yacin Ameur

  2. School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul, 02455, Republic of Korea

    Nam-Gyu Kang & Seong-Mi Seo

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  1. Yacin Ameur
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  2. Nam-Gyu Kang
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  3. Seong-Mi Seo
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Correspondence to Seong-Mi Seo.

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Ameur, Y., Kang, NG. & Seo, SM. On boundary confinements for the Coulomb gas. Anal.Math.Phys. 10, 68 (2020). https://doi.org/10.1007/s13324-020-00406-y

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