Andreas Eberle: Research

Research topics and surveys

Hamiltonian Monte Carlo methods in high dimension
Sampling Crash Course (Simons Institute Boot Camp 2021)
Markov Chain Monte Carlo methods (Hausdorff school MCMC 2020)
Couplings and convergence for Langevin dynamics and Hamiltonian Monte Carlo
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

Francis Lörler (PhD student)
Stefan Oberdörster (PhD student)

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 Heriot-Watt University Edinburgh)
Katharina Schuh (Convergence of McKean-Vlasov processes and Markov Chain Monte Carlo methods for mean-field models, PhD 2022, currently TU Wien)

Recent Preprints

see arXiv

Selected publications

A. Durmus, A. Eberle, A. Guillin, K. Schuh: Sticky nonlinear SDEs and convergence of McKean-Vlasov equations without confinement (final version published in Stochastics and PDE 2023), https://arxiv.org/abs/2201.07652
N.Bou-Rabee, A.Eberle: Mixing time guarantees for unadjusted Hamiltonian Monte Carlo (final version published in Bernoulli 2023, Vol. 29, No. 1, 75-104), arXiv:2105.00887
N.Bou-Rabee, A.Eberle: Couplings for Andersen dynamics (final version published in Annales IHP, Probabilités et Statistique, 2022, Vol. 58, No. 2, 916–944), arXiv:2009.14239
N.Bou-Rabee, A.Eberle: Two-scale coupling for preconditioned Hamiltonian Monte Carlo in infinite dimensions (final version published in Stochastics and Partial Differential Equations, 2021, 9 (1), 207-242), arXiv:1909.07962
A.Durmus, A.Eberle, A.Guillin, R.Zimmer: An elementary approach to uniform in time propagation of chaos (final version published in Proceedings AMS, Volume 148, Number 12, December 2020, Pages 5387–5398), arXiv:1805.11387
N.Bou-Rabee, A.Eberle, R.Zimmer: Coupling and convergence for Hamiltonian Monte Carlo (final version published in Annals of Applied Probability, 2020, Vol. 30, No. 3, 1209-1250), arXiv:1805.00452
A.Eberle, R.Zimmer: Sticky couplings of multidimensional diffusions with different drifts (final version published in Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, 2019, Vol. 55, No. 4, 2370–2394), (pdf)
A.Eberle, A.Guillin, R.Zimmer: Couplings and quantitative contraction rates for Langevin dynamics (published in Annals of Probability, Volume 47, Nr. 4, 2019) (pdf)
A.Eberle, M.B.Majka: Quantitative contraction rates for Markov chains on general state spaces (published in Electronic Journal of Probability, Volume 24, 2019) (pdf)
A.Eberle, A.Guillin, R.Zimmer: Quantitative Harris type theorems for diffusions and McKean-Vlasov processes (final version published in Transactions AMS, Volume 371, Nr. 10, 2019) arXiv:1606.06012
A. Eberle: Reflection couplings and contraction rates for diffusions (final version published in PTRF 166, December 2016, is available at Springer via http://dx.doi.org/10.1007/s00440-015-0673-1)
A. Eberle: Error bounds for Metropolis-Hastings algorithms applied to perturbations of Gaussian measures in high dimensions (Published in at http://dx.doi.org/10.1214/13-AAP926 the Annals of Applied Probability http://www.imstat.org/aap/ 2014)
A. Eberle, C. Marinelli: Quantitative approximations of evolving probability measures and sequential MCMC methods (final version published in PTRF 155, 2013)
A. Eberle: Reflection coupling and Wasserstein contractivity without convexity
(final version published in C.R. Math. Acad. Sci. Paris 349, 2011)