Negative correlation of adjacent Busemann increments
| Autor: | Alevy, Ian, Krishnan, Arjun |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | We consider i.i.d. last-passage percolation on $\mathbb{Z}^2$ with weights having distribution $F$ and time-constant $g_F$. We provide an explicit condition on the large deviation rate function for independent sums of $F$ that determines when some adjacent Busemann function increments are negatively correlated. As an example, we prove that $\operatorname{Bernoulli}(p)$ weights for $p > p^* \approx 0.6504$ satisfy this condition. We prove this condition by establishing a direct relationship between the negative correlations of adjacent Busemann increments and the dominance of the time-constant $g_F$ by the function describing the time-constant of last-passage percolation with exponential or geometric weights. Comment: 22 pages, 4 figures. Generalized the main theorem to pre-Busemann functions, fixed several typos, and added plots of the time-constant |
| Databáze: | arXiv |
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