Research topics and surveys

Coupling approach to kinetic Langevin equation 

Couplings, contractivity and quantitative convergence bounds for diffusions

Metropolis-Hastings algorithms in high dimensions 
Monte Carlo methods for sequences of probability measures 
Analysis on path and loop spaces 
Uniqueness problems for diffusion semigroups 

Research group

  • Katharina Schuh (PhD student)

Recent Preprints

  • A.Eberle, M.B.Majka: Quantitative contraction rates for Markov chains on general state spaces (to appear in Electronic Journal of Probability), arXiv:1808.07033
  • A.Durmus, A.Eberle, A.Guillin, R.Zimmer: An elementary approach to uniform in time propagation of chaos (to appear in Proceedings AMS), arXiv:1805.11387
  • N.Bou-Rabee, A.Eberle, R.Zimmer: Coupling and convergence for Hamiltonian Monte Carlo (Preprint May 2018), arXiv:1805.00452
  • A.Eberle, A.Guillin, R.Zimmer: Couplings and quantitative contraction rates for Langevin dynamics (to appear in Annals of Probability), arXiv:1703.01617
  • A.Eberle, R.Zimmer: Sticky couplings of multidimensional diffusions with different drifts (to appear in Annales IHP (B), Prob. et Stat.), arXiv:1612.06125
  • A.Eberle, A.Guillin, R.Zimmer: Quantitative Harris type theorems for diffusions and McKean-Vlasov processes (to appear in Transactions AMS), arXiv:1606.06012

Selected publications

Reflection couplings and contraction rates for diffusions (final version published in PTRF 166, December 2016, is available at Springer via 
Error bounds for Metropolis-Hastings algorithms applied to perturbations of Gaussian measures in high dimensions (Published in at the Annals of Applied Probability 2014) 
Quantitative approximations of evolving probability measures and sequential MCMC methods (with Carlo Marinelli: final version published in PTRF 155, 2013) 
Reflection coupling and Wasserstein contractivity without convexity
(final version published in C.R. Math. Acad. Sci. Paris 349, 2011)

Previous PhD students

  • Nikolaus Schweizer (Non-asymptotic error bounds for sequential MCMC methods, PhD 2011, currently Tilburg University)
  • Daniel Gruhlke (Transition path sampling and Multi-Level MCMC methods, PhD 2014)
  • Raphael Zimmer (Couplings and Kantorovich contractions with explicit rates for diffusions, PhD 2017)
  • Mateusz B. Majka (Stability of stochastic differential equations with jumps by the coupling method, PhD 2017, currently University of Warwick)