Density of the free additive convolution of multi-cut measures
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866910675427655680 |
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| author | Moreillon, Philippe |
| author_facet | Moreillon, Philippe |
| contents | We consider the free additive convolution semigroup $\lbrace μ^{\boxplus t}:\,t\ge 1\rbrace$ and determine the local behavior of the density of $μ^{\boxplus t}$ 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 endpoints 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_15607 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Density of the free additive convolution of multi-cut measures Moreillon, Philippe Probability 46L54, 60B20, 30A99 We consider the free additive convolution semigroup $\lbrace μ^{\boxplus t}:\,t\ge 1\rbrace$ and determine the local behavior of the density of $μ^{\boxplus t}$ 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 endpoints 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. |
| title | Density of the free additive convolution of multi-cut measures |
| topic | Probability 46L54, 60B20, 30A99 |
| url | https://arxiv.org/abs/2209.15607 |