3 papers
math.CO2026
A computer-assisted proof of Kuperberg's six-cylinder conjecture
Ivan MatiÄ, Rados RadoiÄiÄ
We prove that at most six pairwise non-overlapping infinite unit cylinders can simultaneously touch a unit ball. Six is achievable, so the answer to Kuperberg's question is exactly…
math.PR2026
Higher-order derivatives of first-passage percolation with respect to the environment
Ivan Matic, Rados Radoicic, Dan Stefanica
We introduce and study derivatives in first-passage percolation with edge weights given by i.i.d. random variables supported on . We show that the variance of the passage…
math.PR2026
Fourier levels and almost sure bounds on higher-order derivatives in first-passage percolation
Ivan Matic, Rados Radoicic, Dan Stefanica
The variance of first-passage percolation admits a decomposition into Fourier levels indexed by the order of environment derivatives. These Fourier levels capture how local perturb…