Global asymptotics for $β$-Krawtchouk corners processes via multi-level loop equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917622831906816 |
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| author | Dimitrov, Evgeni Knizel, Alisa |
| author_facet | Dimitrov, Evgeni Knizel, Alisa |
| contents | We introduce a two-parameter family of probability distributions, indexed by $β/2 = θ> 0$ and $K \in \mathbb{Z}_{\geq 0}$, that are called $β$-Krawtchouk corners processes. These measures are related to Jack symmetric functions, and can be thought of as integrable discretizations of $β$-corners processes from random matrix theory, or alternatively as non-determinantal measures on lozenge tilings of infinite domains. We show that as $K$ tends to infinity the height function of these models concentrates around an explicit limit shape, and prove that its fluctuations are asymptotically described by a pull-back of the Gaussian free field, which agrees with the one for Wigner matrices. The main tools we use to establish our results are certain multi-level loop equations introduced in our earlier work arXiv:2108.07710. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17895 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global asymptotics for $β$-Krawtchouk corners processes via multi-level loop equations Dimitrov, Evgeni Knizel, Alisa Probability Mathematical Physics 82C41, 52C20 We introduce a two-parameter family of probability distributions, indexed by $β/2 = θ> 0$ and $K \in \mathbb{Z}_{\geq 0}$, that are called $β$-Krawtchouk corners processes. These measures are related to Jack symmetric functions, and can be thought of as integrable discretizations of $β$-corners processes from random matrix theory, or alternatively as non-determinantal measures on lozenge tilings of infinite domains. We show that as $K$ tends to infinity the height function of these models concentrates around an explicit limit shape, and prove that its fluctuations are asymptotically described by a pull-back of the Gaussian free field, which agrees with the one for Wigner matrices. The main tools we use to establish our results are certain multi-level loop equations introduced in our earlier work arXiv:2108.07710. |
| title | Global asymptotics for $β$-Krawtchouk corners processes via multi-level loop equations |
| topic | Probability Mathematical Physics 82C41, 52C20 |
| url | https://arxiv.org/abs/2403.17895 |