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- Mario Ullrich
- Random Struct. Algorithms
- 2013

We prove that the spectral gap of the Swendsen-Wang process for the Potts model on graphs with bounded degree is bounded from below by some constant times the spectral gap of any single-spinâ€¦ (More)

- Mario Ullrich
- SIAM J. Discrete Math.
- 2014

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 per step. For thisâ€¦ (More)

- Mario Ullrich
- ArXiv
- 2012

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 16m logm times the spectral gap of the single-bond (orâ€¦ (More)

- Aicke Hinrichs, Erich Novak, Mario Ullrich, Henryk Wozniakowski
- Math. Comput.
- 2014

We prove the curse of dimensionality for multivariate integration of Ck functions. The proofs are based on volume estimates for k = 1 together with smoothing by convolution. This allows us to obtainâ€¦ (More)

We prove that heat-bath chains (which we define in a general setting) have no negative eigenvalues. Two applications of this result are presented: one to single-site heat-bath chains for spin systemsâ€¦ (More)

- Aicke Hinrichs, Erich Novak, Mario Ullrich
- Journal of Approximation Theory
- 2014

We consider the problem of integration of d-variate analytic functions defined on the unit cube with directional derivatives of all orders bounded by 1. We prove that the Clenshaw Curtis Smolyakâ€¦ (More)

- Medina Ablikim, M. N. Achasov, +410 authors Jianfei Zou
- 2015

M. Ablikim, M. N. Achasov, X. C. Ai, O. Albayrak, M. Albrecht, D. J. Ambrose, A. Amoroso, F. F. An, Q. An, J. Z. Bai, R. Baldini Ferroli, Y. Ban, D. W. Bennett, J. V. Bennett, M. Bertani, D. Bettoni,â€¦ (More)

- Mario Ullrich, Tino Ullrich
- SIAM J. Numerical Analysis
- 2016

We prove upper bounds on the order of convergence of Frolovâ€™s cubature formula for numerical integration in function spaces of dominating mixed smoothness on the unit cube with homogeneous boundaryâ€¦ (More)

- Erich Novak, Mario Ullrich, Henryk Wozniakowski
- J. Complexity
- 2015

We analyze univariate oscillatory integrals for the standard Sobolev spaces Hs of periodic and non-periodic functions with an arbitrary integer s â‰¥ 1. We find matching lower and upper bounds on theâ€¦ (More)

We prove positivity of the Markov operators that correspond to the hit-and-run algorithm, random scan Gibbs sampler, slice sampler and Metropolis algorithm with positive proposal. In particular, theâ€¦ (More)