On Properties of Optimal Paths in First-Passage Percolation
| Autor: | Shuta Nakajima |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Atom (order theory) Statistical and Nonlinear Physics First passage percolation Mathematical proof 01 natural sciences 010305 fluids & plasmas Distribution (mathematics) Mathematics::Probability Intersection Resampling 0103 physical sciences 010306 general physics Mathematical Physics Mathematics |
| Zdroj: | Journal of Statistical Physics. 174:259-275 |
| ISSN: | 1572-9613 0022-4715 |
| DOI: | 10.1007/s10955-018-2179-6 |
| Popis: | In this paper, we study some properties of optimal paths in the first passage percolation on $$\mathbb {Z}^d$$ and show the following: (i) the number of optimal paths has an exponentially growth if the distribution has an atom; (ii) the means of intersection and union of optimal paths are linear in the distance. For the proofs, we use the resampling argument introduced in van den Berg and Kesten (Ann Appl Probab 3:56–80, 1993) with suitable adaptions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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