5 papers
Littlewood's mutually touching cylinders: the maximum is seven
Ivan Matić, Radoš Radoičić, Andreas Spomer
We give a computer-assisted proof that eight congruent infinite circular cylinders in cannot touch pairwise. Since seven such cylinders exist, the maximum number of…
Insertion and expansion of cylinders around the unit ball
Ivan Matić, Radoš Radoičić, Andreas Spomer
A unit ball is surrounded with a ring of equal infinite circular cylinders. Each cylinder touches the ball and its two neighbors. Can one more cylinder of the same radius be ad…
A computer-assisted proof of Kuperberg's six-cylinder conjecture
Ivan Matić, Rados Radoičić
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…
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…
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…