Uniform convergence to the Airy line ensemble
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
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| _version_ | 1866916218826391552 |
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| author | Dauvergne, Duncan Nica, Mihai Virág, Bálint |
| author_facet | Dauvergne, Duncan Nica, Mihai Virág, Bálint |
| contents | We show that classical integrable models of last passage percolation and the related nonintersecting random walks converge uniformly on compact sets to the Airy line ensemble. Our core approach is to show convergence of nonintersecting Bernoulli random walks in all feasible directions in the parameter space. We then use coupling arguments to extend convergence to other models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_10160 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Uniform convergence to the Airy line ensemble Dauvergne, Duncan Nica, Mihai Virág, Bálint Probability Mathematical Physics We show that classical integrable models of last passage percolation and the related nonintersecting random walks converge uniformly on compact sets to the Airy line ensemble. Our core approach is to show convergence of nonintersecting Bernoulli random walks in all feasible directions in the parameter space. We then use coupling arguments to extend convergence to other models. |
| title | Uniform convergence to the Airy line ensemble |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/1907.10160 |