Negative correlation of adjacent Busemann increments · arXivDesk
2102.06337Feb 12, 202122 pages, 4 figures. Generalized the main theorem to pre-Busemann functions, fixed several typos, and added plots of the time-constant
Negative correlation of adjacent Busemann increments
We consider i.i.d. last-passage percolation on Z2 with weights having distribution F and time-constant gF. We provide an explicit condition on the large deviation rate function for independent sums of F
Nearby in the stack
that determines when some adjacent Busemann function increments are negatively correlated. As an example, we prove that
Bernoulli(p)
weights for
p>p∗≈0.6504
satisfy this condition. We prove this condition by establishing a direct relationship between the negative correlations of adjacent Busemann increments and the dominance of the time-constant
gF
by the function describing the time-constant of last-passage percolation with exponential or geometric weights.