Order of the Variance in the Discrete Hammersley Process with Boundaries
| Autor: | Nicos Georgiou, Federico Ciech |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Probability (math.PR)
Mathematical analysis Statistical and Nonlinear Physics 01 natural sciences 010305 fluids & plasmas Piecewise linear function Bernoulli's principle Boundary model Lattice (order) 0103 physical sciences FOS: Mathematics Shape function QA 010306 general physics Mathematics - Probability Mathematical Physics Mathematics |
| Zdroj: | Journal of Statistical Physics. 176:591-638 |
| ISSN: | 1572-9613 0022-4715 |
| Popis: | We discuss the order of the variance on a lattice analogue of the Hammersley process with boundaries, for which the environment on each site has independent, Bernoulli distributed values. The last passage time is the maximum number of Bernoulli points that can be collected on a piecewise linear path, where each segment has strictly positive but finite slope. We show that along characteristic directions the order of the variance of the last passage time is of order $N^{2/3}$ in the model with boundary. These characteristic directions are restricted in a cone starting at the origin, and along any direction outside the cone, the order of the variance changes to $O(N)$ in the boundary model and to $O(1)$ for the non-boundary model. This behaviour is the result of the two flat edges of the shape function. 47 pages, 4 figures |
| Databáze: | OpenAIRE |
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