Ciech-Georgiou2019_Article_OrderOfTheVarianceInTheDiscret.pdf (793.28 kB)
Order of the variance in the discrete Hammersley process with boundaries
Version 2 2023-06-12, 09:07
Version 1 2023-06-09, 17:54
journal contribution
posted on 2023-06-12, 09:07 authored by Federico Ciech, Nicos GeorgiouNicos GeorgiouWe 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.
Funding
The flat edge in last passage percolation; G2031; EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL; EP/P021409/1
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- Published
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- Published version
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Journal of Statistical PhysicsISSN
0022-4715Publisher
SpringerExternal DOI
Department affiliated with
- Mathematics Publications
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- Probability and Statistics Research Group Publications
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- Yes
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- Yes
Legacy Posted Date
2019-05-24First Open Access (FOA) Date
2019-06-07First Compliant Deposit (FCD) Date
2019-05-23Usage metrics
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