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Lower bounds for point-to-point wandering exponents in Euclidean first-passage percolation
- Part of
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- Journal:
- Journal of Applied Probability / Volume 37 / Issue 4 / December 2000
- Published online by Cambridge University Press:
- 14 July 2016, pp. 1061-1073
- Print publication:
- December 2000
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- Article
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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.
. Here, for Euclidean models in dimension 