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Martin Slowik, Dr.

Currently I am holding a PostDoc position in the group of Prof. Dr. Jochen Blath financed by the DFG Priority Program 1590 "Probabilistic Structures in Evolution".

Office hour: by appointment (MA 769)

Teaching

Lectures

Lectures at University Giessen
Spring 2018
 Markov Proxesse, Konvergenz  and Metastabilität (4 SWS) MSc/PhD
Stochastik II (4 SWS) BSc
Lectures at TU Berlin
Spring 2017
 Maß- und Integrationstheorie (4 SWS) MSc
Fall 2016
Markov processes and metastability (2 SWS) BSc/MSc
Spring 2015
Mathematik II für Ökonomen (2 SWS) BSc
Fall 2014
Mathematik I für Ökonomen (2 SWS) BSc
Spring 2012
Mathematik II für Brauerei- und Brennereitechnologen (3 SWS) BSc

Exercise classes and seminars

Exercise classes and seminars at TU Berlin
WiSe 2017
Analysis I für Ingenieurswissenschaften
SoSe 2017
Statistik
WiSe 2016
Stochastische Modelle
Seminar "Wechselwirkende Teilchensysteme”
SoSe 2016
Differentialgleichungen für Ingenieure
Seminar  "Stochastische Prozesse und ihre Anwendungen”
WiSe 2015
Early Bird I für Ingenieure
SoSe 2015
Mathematik II für Ökonomen
WiSe 2014
Mathematik I für Ökonomen
SoSe 2012
Seminar "Ausgewählte Kapitel der Wahrscheinlickeitstheorie"
Exercise classes and seminars at University Bonn
SoSe 2011
Seminar "Markovketten und stochastische Algorithmen”
SoSe 2010
Angewandte Stochastik und Statistik
Seminar "Markovketten und stochastische Algorithmen”
Seminar "Angewandte Stochastik"
WiSe 2009
Seminar "Numerische stochastische Analysis"
SoSe 2009
Algorithmische Mathematik II

Research topics

  • metastable behaviour of Markov processes
  • functional inequalities related to the longtime behaviour of stochastic processes
  • scaling limits of stochastic processes in random media
  • population genetics

Peer reviewed

  1. A. Schlichting, M. Slowik.
    Poincaré and logarithmic Sobolev constants for metastable Markov chains via capacitary inequalities. Ann. Appl. Probab., 29, no. 6, 3438-3488 (2019). journal arXiv
  2. S. Andres, J.-D. Deuschel, M. Slowik.
    Heat kernel estimates and intrinsic metric for random walks with general speed measure under degenerate conductances. Electron. Commun. Probab. 24, no. 5, 1-17 (2019). journal  arXiv
  3. F. Flegel, M. Heida, M. Slowik.
    Homogenization theory for the random conductance model with degenerate ergodic weights and unbounded-range jumps. Ann. Inst. Henri Poincaré Probab. Stat. 55, no. 3, 1226-1257 (2019). journal  arXiv
  4. S. Andres, A. Chiarini, J.-D. Deuschel, M. Slowik.
    Quenched invariance principle for random walks with time-dependent ergodic degenerate weights. Ann. Probab. 46, no. 1, 302–336 (2018). journal arXiv
  5. J.-D. Deuschel, T. A. Nguyen, M. Slowik.
    Quenched invariance principles for the random conductance model on a random graph with degenerate weights. Probab. Theory Related Fields 170, no. 1-2, 363–386 (2018). journal arXiv
  6. J.-D. Deuschel, P. Friz, M. Maurelli, M. Slowik.
    The enhanced Sanov theorem and propagation of chaos. Stochastic Process. Appl., 128, no. 7, 2228–2269 (2018). journal arXiv
  7. J.-D. Deuschel, M. Slowik.
    Invariance principle for the one-dimensional dynamic random conductance model under moment conditions. RIMS Kokyuroku Bessatsu B59, 69–84 (2016). arXiv
  8. S. Andres, J.-D. Deuschel, M. Slowik.
    Heat kernel estimates for random walks with degenerate weights. Electron. J. Probab. 21, no. 33, 1–21 (2016). journal arXiv
  9. S. Andres, J.-D. Deuschel, M. Slowik.
    Harnack inequalities on weighted graphs and some applications to the random conductance model. Probab. Theory Related Fields 164, no. 3–4, 931–977 (2016). journal arXiv
  10. S. Andres, J.-D. Deuschel, M. Slowik.
    Invariance principle for the random conductance model in a degenerate ergodic environment. Ann. Probab. 43, no. 4, 1866–1891 (2015). journal arXiv
  11. P. Benner, V. Sima, M. Slowik.
    Evaluation of the Linear Matrix Equation Solvers in SLICOT. JNAIAM J. Numer. Anal. Ind. Appl. Math. 2, no. 1–2, 11–34 (2007) journal

Preprints

  1. S. Andres, A. Chiarini, M. Slowik
    Quenched local limit theorem for random walks among time-dependent degenerate conductances on random graphs. arXiv:2001.10740, 1-29 (2020). arXiv
  1. S. Andres, J.-D. Deuschel, M. Slowik.
    Green kernel asymptotics for two-dimensional random walks under random conductances. arXiv:1808.08126, 1-16 (2018). arXiv
  2. M. Slowik.
    A note on variational representations of capacities for reversible and non-reversible Markov chains. Preprint TU Berlin, 1–13 (2012).

Work in progress

  1. J.-D. Deuschel, T. Kumagai, M. Slowik
    Gradient estimates of the heat kernel in the dynamic RCM. in preparation.

Thesis

  1. M. Slowik. Contributions to the Potential Theoretic Approach to Metastability with Applications to the Random Field Curie-Weiss-Potts Model. PhD thesis, TU Berlin, 2012. DepositOnce

Organization of events

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Technische Universität Berlin
Institute of Mathematics
Faculty Mathematics and Natural Sciene
sec. MA 7-5
Room MA 769
Straße des 17. Juni 136
10623 Berlin
tel.:+49 30 314-23606