Scaling limits of random normal matrix processes at singular boundary\n points

2015/10/29 by Yacin Ameur, Namgyu Kang, Ameur, Yacin +5 · 1 citation
Mathematics · Physics and Astronomy · #30C40 #30D15 #35R09 #81T40 #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 60B20 #Probability (math.PR) #Random Matrices and Applications #Secondary: 60G55 #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1510.08723

openalex publication_date 2015/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a method for taking microscopic limits of normal matrix ensembles. We\napply this method to study the behaviour near certain types of singular points\non the boundary of the droplet. Our investigation includes ensembles without\nrestrictions near the boundary, as well as hard edge ensembles, where the\neigenvalues are confined to the droplet. We establish in both cases existence\nof new types of determinantal point fields, which differ from those which can\nappear at a regular boundary point, or in the bulk.\n

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