5 papers
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…
A generalization of the rational rough Heston approximation
Jim Gatheral, Radoš Radoičić
Previously, in [GR19], we derived a rational approximation of the solution of the rough Heston fractional ODE in the special case λ= 0, which corresponds to a pure power-law kernel…
The Zumbach effect under rough Heston
Omar El Euch, Jim Gatheral, Radoš Radoičić +1
Previous literature has identified an effect, dubbed the Zumbach effect, that is nonzero empirically but conjectured to be zero in any conventional stochastic volatility model. Ess…