Monotone max-convolution and subordination functions for free max-convolution
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915922824921088 |
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| author | Ueda, Yuki |
| author_facet | Ueda, Yuki |
| contents | We show that the distribution of the spectral maximum of monotonically independent self-adjoint operators coincides with the classical max-convolution of their distributions. In free probability, it was proven that for any probability measures $σ,μ$ on $\mathbb{R}$ there is a unique probability measure $\mathbb{A}_σ(μ)$ satisfying $σ\boxplus μ= σ\triangleright \mathbb{A}_σ(μ)$, where $\boxplus$ and $\triangleright$ are free and monotone additive convolutions, respectively. We recall that the reciprocal Cauchy transform of $\mathbb{A}_σ(μ)$ is the subordination function for free additive convolution. Motivated by this analogy, we introduce subordination functions for free max-convolution and prove their existence and structural properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13972 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monotone max-convolution and subordination functions for free max-convolution Ueda, Yuki Operator Algebras Probability Spectral Theory 46L54, 46L53 We show that the distribution of the spectral maximum of monotonically independent self-adjoint operators coincides with the classical max-convolution of their distributions. In free probability, it was proven that for any probability measures $σ,μ$ on $\mathbb{R}$ there is a unique probability measure $\mathbb{A}_σ(μ)$ satisfying $σ\boxplus μ= σ\triangleright \mathbb{A}_σ(μ)$, where $\boxplus$ and $\triangleright$ are free and monotone additive convolutions, respectively. We recall that the reciprocal Cauchy transform of $\mathbb{A}_σ(μ)$ is the subordination function for free additive convolution. Motivated by this analogy, we introduce subordination functions for free max-convolution and prove their existence and structural properties. |
| title | Monotone max-convolution and subordination functions for free max-convolution |
| topic | Operator Algebras Probability Spectral Theory 46L54, 46L53 |
| url | https://arxiv.org/abs/2512.13972 |