Article contents
Lower bounds for point-to-point wandering exponents in Euclidean first-passage percolation
Published online by Cambridge University Press: 14 July 2016
Abstract
In first-passage percolation models, the passage time T(0,L) from the origin to a point L is expected to exhibit deviations of order |L|χ from its mean, while minimizing paths are expected to exhibit fluctuations of order |L|ξ away from the straight line segment . Here, for Euclidean models in dimension d, we establish the lower bounds ξ ≥ 1/(d+1) and χ ≥(1-(d-1)ξ)/2. Combining this latter bound with the known upper bound ξ ≤ 3/4 yields that χ ≥ 1/8 for d=2.
- Type
- Research Papers
- Information
- Copyright
- Copyright © by the Applied Probability Trust 2000
Footnotes
Research supported in part by NSF Grant DMS-98-15226.
References
- 2
- Cited by