53 citations · 640 across the 36 of their papers we have counts for
4 papers · 1 filter
Positivity of hit-and-run and related algorithms
Daniel Rudolf, Mario Ullrich
We prove positivity of the Markov operators that correspond to the hit-and-run algorithm, random scan Gibbs sampler, slice sampler and an Metropolis algorithm with positive proposa…
The Curse of Dimensionality for Numerical Integration of Smooth Functions
Aicke Hinrichs, Erich Novak, Mario Ullrich +1
We prove the curse of dimensionality for multivariate integration of C^r functions: The number of needed function values to achieve an error ε is larger than c_r (1+γ)^d for ε\le ε…
Rapid mixing of Swendsen-Wang and single-bond dynamics in two dimensions
Mario Ullrich
We prove that the spectral gap of the Swendsen-Wang dynamics for the random-cluster model on arbitrary graphs with m edges is bounded above by 16 m log m times the spectral gap of…
Swendsen-Wang is faster than single-bond dynamics
Mario Ullrich
We prove that the spectral gap of the Swendsen-Wang dynamics for the random-cluster model is larger than the spectral gap of a single-bond dynamics, that updates only a single edge…