2 problems

0 votes0 replies0 views
Conjecture on the absence of a linear piece in the shape function
Shape-function linearity conjecture. For $\kappa$ sufficiently close to $-1$ , the shape function $\Lambda$ does not have a linear piece.
Conjectureopenlast-passage-percolation random-environments shape-functionsarXiv posted 2 days ago
0 votes0 replies0 views
Steele–Zhang's differentiability conjecture for the Bernoulli time constant
Let $t(e)$ be Bernoulli edge weights, let $\mathbf{e}_1$ denote the first coordinate vector, and write $\mu_{\mathbf{e}_1}(a)=\mu^{(a)}(\mathbf{e}_1)$ for the shape function in dir…
Conjectureopenbernoulli-percolation first-passage-percolation shape-functionsarXiv posted 2 days ago

Conjecture on the absence of a linear piece in the shape function