Gaussian Multiplicative Chaos for i.i.d. matrices
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866916061448765440 |
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| author | Cipolloni, Giorgio Landon, Benjamin |
| author_facet | Cipolloni, Giorgio Landon, Benjamin |
| contents | We consider $N\times N$ matrices $X$ with independent, identically distributed entries, and prove that the sequence of measures $\frac{ | \det (X-z)|^γ}{\mathbb{E}[ | \det (X-z)|^γ]}$ converge to the Gaussian Multiplicative Chaos in the full subcritical regime $γ\in (0, 2 \sqrt{2})$ as $N \to \infty$. Our result holds for both symmetry classes and in particular is new even for real Ginibre matrices, and is the first such convergence for any non-invariant ensemble of random matrices. We also establish the asymptotics for the $K$-point function of $| \det (X-z)|$ at any collection of mesoscopically separated points $z_i$. Our methods are analytic and probabilistic in nature, relying in part on the dynamical approach based on Dyson Brownian motion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29962 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gaussian Multiplicative Chaos for i.i.d. matrices Cipolloni, Giorgio Landon, Benjamin Probability Mathematical Physics We consider $N\times N$ matrices $X$ with independent, identically distributed entries, and prove that the sequence of measures $\frac{ | \det (X-z)|^γ}{\mathbb{E}[ | \det (X-z)|^γ]}$ converge to the Gaussian Multiplicative Chaos in the full subcritical regime $γ\in (0, 2 \sqrt{2})$ as $N \to \infty$. Our result holds for both symmetry classes and in particular is new even for real Ginibre matrices, and is the first such convergence for any non-invariant ensemble of random matrices. We also establish the asymptotics for the $K$-point function of $| \det (X-z)|$ at any collection of mesoscopically separated points $z_i$. Our methods are analytic and probabilistic in nature, relying in part on the dynamical approach based on Dyson Brownian motion. |
| title | Gaussian Multiplicative Chaos for i.i.d. matrices |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2605.29962 |