Work

Density of the Free Additive Convolution of Multi-cut Measures

Year: 2024

Type: article

Abstract: We consider the free additive convolution semigroup $\lbrace \mu ^{\boxplus t}:\,t\ge 1\rbrace $ and determine the local behavior of the density of $\mu ^{\boxplus t}$ at the endpoints and at any singular point of its support. We then study the free additive convolution of two multi-cut probability measures and show that its density decays either as a square root or as a cubic root at any endpoint of its support. The probability measures considered in this paper satisfy a power law behavior with exponents strictly between $-1$ and $1$ at the endpoints of their supports.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnae229

Author: Philippe Moreillon

Institution: KTH Royal Institute of Technology

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,534

Funders: Royal Swedish Academy of Sciences, Swedish Foundation for International Cooperation in Research and Higher Education