Large deviations of geodesic midpoint fluctuations in last-passage percolation with general i.i.d. weights
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915134245437440 |
|---|---|
| author | Alberts, Tom Basu, Riddhipratim Groathouse, Sean Shen, Xiao |
| author_facet | Alberts, Tom Basu, Riddhipratim Groathouse, Sean Shen, Xiao |
| contents | The study of transversal fluctuations of the optimal path is a crucial aspect of the Kardar-Parisi-Zhang (KPZ) universality class. In this work, we establish the large deviation limit for the midpoint transversal fluctuations in a general last-passage percolation (LPP) model with mild assumption on the i.i.d. weights. The rate function is expressed in terms of the right tail large deviation rate function of the last-passage value and the shape function. When the weights are chosen to be i.i.d. exponential random variables, our result verifies a conjecture communicated to us by Liu [Liu'22], showing the asymptotic probability of the geodesic from $(0,0)$ to $(n,n)$ following the corner path $(0,0) \to (n,0) \to (n,n)$ is $({4}/{e^2})^{n+o(n)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00942 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large deviations of geodesic midpoint fluctuations in last-passage percolation with general i.i.d. weights Alberts, Tom Basu, Riddhipratim Groathouse, Sean Shen, Xiao Probability Mathematical Physics 60K35, 60K37 The study of transversal fluctuations of the optimal path is a crucial aspect of the Kardar-Parisi-Zhang (KPZ) universality class. In this work, we establish the large deviation limit for the midpoint transversal fluctuations in a general last-passage percolation (LPP) model with mild assumption on the i.i.d. weights. The rate function is expressed in terms of the right tail large deviation rate function of the last-passage value and the shape function. When the weights are chosen to be i.i.d. exponential random variables, our result verifies a conjecture communicated to us by Liu [Liu'22], showing the asymptotic probability of the geodesic from $(0,0)$ to $(n,n)$ following the corner path $(0,0) \to (n,0) \to (n,n)$ is $({4}/{e^2})^{n+o(n)}$. |
| title | Large deviations of geodesic midpoint fluctuations in last-passage percolation with general i.i.d. weights |
| topic | Probability Mathematical Physics 60K35, 60K37 |
| url | https://arxiv.org/abs/2502.00942 |