5 problems

Higher-order derivative probability-ratio conjecture in the torus model
Derivative probability-ratio conjecture. There exists a constant $\theta\in(0,d/2)$ such that
openFrom papersfirst-passage-percolation random-environment-derivatives torus-model
0 responses
3
Positive-drift conjecture for higher-order environment derivatives
Positive-drift conjecture. There exists $\theta_k\in(0,1)$ such that, for most reasonable $k$ -edge sets $S$ and every positive $m$ ,
openFrom papersfirst-passage-percolation probability random-environment-derivatives
0 responses
5
Conjecture on nonnegative expected higher-order derivatives
Nonnegative-expectation conjecture. For most sets $S$ , the expected value of the higher-order derivative is non-negative:
openFrom papersfirst-passage-percolation random-environment-derivatives
0 responses
3
Conjecture on the total second-order derivative mass in first-passage percolation
Second-order mass conjecture. There exists a constant $C$ independent of $N$ such that
openFrom papersfirst-passage-percolation random-environment-derivatives torus-model
0 responses
6
Conjecture on comparable probabilities of essential and influential edges
Comparability conjecture. There exists a constant $C$ independent of $n$ such that
openFrom papersfirst-passage-percolation geodesics random-environment-derivatives
0 responses
7

Higher-order derivative probability-ratio conjecture in the torus model