scholarly journals Upper Tail Large Deviations in First Passage Percolation

2021 ◽  
Vol 74 (8) ◽  
pp. 1577-1640
Author(s):  
Riddhipratim Basu ◽  
Allan Sly ◽  
Shirshendu Ganguly
2003 ◽  
Vol 13 (4) ◽  
pp. 1601-1614 ◽  
Author(s):  
Yu Zhang ◽  
Yunshyong Chow

2011 ◽  
Vol 48 (02) ◽  
pp. 366-388 ◽  
Author(s):  
Eckhard Schlemm

We consider the first passage percolation problem on the random graph with vertex set N x {0, 1}, edges joining vertices at a Euclidean distance equal to unity, and independent exponential edge weights. We provide a central limit theorem for the first passage times l n between the vertices (0, 0) and (n, 0), thus extending earlier results about the almost-sure convergence of l n / n as n → ∞. We use generating function techniques to compute the n-step transition kernels of a closely related Markov chain which can be used to explicitly calculate the asymptotic variance in the central limit theorem.


Sign in / Sign up

Export Citation Format

Share Document