Coalescence estimates for the corner growth model with exponential weights
| Autor: | Timo Seppäläinen, Xiao Shen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Coalescence (physics) Logarithm Geodesic Integrable system Probability (math.PR) coalescence exit time last-passage percolation fluctuation exponent Upper and lower bounds random growth model Exponential function 60K37 60K35 Exponent FOS: Mathematics Applied mathematics 60K35 60K37 Statistics Probability and Uncertainty Kardar-Parisi-Zhang Mathematics - Probability Order of magnitude geodesic Mathematics |
| Zdroj: | Electron. J. Probab. |
| Popis: | We establish estimates for the coalescence time of semi-infinite directed geodesics in the planar corner growth model with i.i.d. exponential weights. There are four estimates: upper and lower bounds on the probabilities of both fast and slow coalescence on the correct spatial scale with exponent $3/2$. Our proofs utilize a geodesic duality introduced by Pimentel and properties of the increment-stationary last-passage percolation process. For fast coalescence our bounds are new and they have matching optimal exponential order of magnitude. For slow coalescence we reproduce bounds proved earlier with integrable probability inputs, except that our upper bound misses the optimal order by a logarithmic factor. Comment: Fixed an error in the proof of Theorem 4.1 from the previously published version. Added acknowledgments. (34 pages, 23 figures) |
| Databáze: | OpenAIRE |
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