Department Mathematik



Markus Heydenreich

Professor of Applied Mathematics

Mathematisches Institut
der Universität München
Theresienstr. 39
D-80333 München

Email: m.heydenreich(at)

Tel:   +49 (0)89   2180 4478
Fax:  +49 (0)89   2180 4466
Office: B-wing, 2nd floor, room 216

Stochastics and Mathematical Finance Group


 Stochastic processes (winter term 2016/17), more information is on this webpage


I am a probabilist with a research focus on the study of random discrete objects.
Some keywords characterizing my activities are
  • phase transitions in models of statistical mechanics; mean-field behavious; lace expansion
  • long-range order of discrete models in continuum space; symmetry breaking; crystallization
  • spatial random graph models
  • random walk in dynamic random environment

Research seminars in Munich

Oberseminar Wahrscheinlichkeitstheorie organized jointly with TUM

Mathematical Colloquium at LMU Munich

Office hour

Term: Wednesday 2:00-3:00 p.m.
Term break: Office hour by appointment, please.

Those seeking an advisor for their bachelor- or masterthesis are kindly requested to indicate the desired topic and relevant course background by email.

Organization of conferences and workshops

Probability Day Erlangen-München, joint annual event of FAU Erlangen-Nürnberg, TU München and LMU München.
Workshop Trends in Mathematical Crystallization at Warwick University (UK), May 3-6, 2016. Jointly organized with Stefan Adams (Warwick), Sabine Jansen (Bochum), and Frank den Hollander (Leiden).
[Workshop website]
Logo KWG
The 51st Netherlands Mathematical Congress takes place in Leiden April 14-15, 2015 under the auspices of the Koninklijk Wiskundig Genootschap.
[Congress website]
Workshop Random walks in random environment, the 12th workshop in the Young European Probabilists series, organized jointly with Alexander Drewitz (New York) at EURANDOM in Eindhoven; March 23-27, 2015. [Workshop website]
Workshop Mathematical Facets of Crystallization at the Lorentz Center in Leiden September 8-12, 2014. Jointly organized with Sabine Jansen (Bochum) and Frank den Hollander (Leiden).
[Workshop website]
Logo Lorentz
Logo SWI
Studygroup Mathematics with Industry 2013, at the Lorentz Center in Leiden, January 28 - February 1, 2013.
Website Studygroup
Workshop The expanding art of expansions at EURANDOM in Eindhoven February 14-17, 2012. Jointly organized with Remco van der Hofstad (Eindhoven) and Roberto Fernandez (Utrecht).
[Workshop website]

Lecture Notes

  • M. Heydenreich and R. van der Hofstad,
    Progress in high-dimensional percolation and random graphs (267 pages, March 2017).

Preprints and articles

    My most recent preprints are on [my-preprints@arXiv]

  • S. Handa, M. Heydenreich, and A. Sakai,
    Mean-field bound on the 1-arm exponent for Ising ferromagnets in high dimensions.
    Preprint, 14 pages.

  • M. Heydenreich, T. Hulshof, and J. Jorritsma,
    Structures in supercritical scale-free percolation.
    Preprint, 28 pages. To appear in Annals of Applied Probability.

  • S. Bethuelsen and M. Heydenreich,
    Random Walks on Attractive Spin-Flip Dynamics: Law of Large Numbers and Large Deviation Estimates.
    Preprint, 25 pages. To appear in Stochastic Processes and Applications.
    [article@ScienceDirect]   [preprint@arXiv

  • J. van den Berg, J. E. Björnberg, and M. Heydenreich,
    Sharpness versus robustness of the percolation transition in 2d contact processes.
    Stochastic Processes and Applications 125(2):513-537 (2015).
    [article@ScienceDirect]   [preprint@arXiv

  • M. Heydenreich, F. Merkl, and S.W.W. Rolles,
    Spontaneous breaking of rotational symmetry in the presence of defects.
    Electronic Journal of Probability 19, no. 111: 1-17 (2014).
    [article@EJP]   [preprint@arXiv]

  • M. Heydenreich, R. van der Hofstad, and T. Hulshof,
    Random walk on the high-dimensional IIC. 
    Communications in Mathematical Physics 329 (1): 57-115 (2014). 
    [article@SpringerLink]   [preprint@arXiv]

  • M. Heydenreich, R. van der Hofstad, and T. Hulshof,
    High-dimensional incipient infinite cluster revisited.
    Journal of Statistical Physics 155 (5): 966-1025 (2014).
    [article@SpringerLink]   [preprint@arXiv]

  • M. Heydenreich and R. van der Hofstad,
    Random graph asymptotics on high-dimensional tori. II. Volume, diameter and mixing time.
    Probability Theory and Related Fields 149 (3-4): 397-415 (2011).
    [article@SpringerLink] (open access)   [preprint@arXiv]

  • M. Heydenreich,
    Long-range self-avoiding walk converges to alpha-stable processes.
    Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques 47 (1): 20-42 (2011).
    [article@projecteuclid]   [preprint@arXiv]

  • M. Heydenreich, R. van der Hofstad, and G. Radulov,
    Functionals of Brownian Bridges arising in the current mismatch in D/A converters.
    Probability in the Engineering and Informational Sciences 23 (1): 149-172 (2009).
    [article@CambridgeJournals]   [preprint@arXiv]

  • M. Heydenreich, R. van der Hofstad, and A. Sakai,
    Mean-field behavior for long- and finite range
    Ising model, percolation and self-avoiding walk.
    Journal of Statistical Physics 132 (6): 1001-1049 (2008). 
    [article@SpringerLink] (open access)   [preprint@arXiv]

  • G. Radulov, M. Heydenreich, R. van der Hofstad, J.A. Hegt, and A.H.M. van Roermund,
    Brownian Bridge based statistical analysis of the DAC INL caused by current mismatch.
    IEEE Transactions on Circuits and Systems II: Express Briefs 54 (2): 146-150 (2007). 

  • M. Heydenreich and R. van der Hofstad,
    Random graph asymptotics on high-dimensional tori.
    Communications in Mathematical Physics 270 (2): 335-358 (2007). 
    [article@SpringerLink]   [preprint@arXiv]   [poster]

  • J. Gärtner and M. Heydenreich,
    Annealed asymptotics for the parabolic Anderson model with a moving catalyst.
    Stochastic Processes and their Applications 116 (11): 1511-1529 (2006). 
    [article@ScienceDirect]   [preprint]

Conference proceedings, etc.

  • Proceedings of the 90th European Studygroup Mathematics with Industry, Leiden, The Netherlands, January 28-February 1, 2013.
    Edited by M. Heydenreich, S. Hille, V. Rottschäfer, F. Spieksma, and E. Verbitskiy.

  • Ph. Cara, I. Corro Ramos, T.J. Dijkema, L. Hakobyan, M. Heydenreich, E. Jochemsz, T. Mussche, M. Popoviciu-Draisma, J.A.C. Resing (2006).
    Divide and conquer: optimizing the release policy of software versions.
    In E.R. Fledderus, R.W. van der Hofstad, E. Jochemsz, J. Molenaar, T.J.J. Mussche, M.A. Peletier, G. Prokert, Mathematics in Industry (Proceedings 55th European Studygroup Mathematics with Industry, ESGI55/SWI2006, Eindhoven, The Netherlands, January 30-February 3, 2006) Eindhoven: Technische Universiteit Eindhoven.


  • Diplom-Wirtschaftsmathematik (dipl. math. oec.), Technische Universität Berlin, 2004     [Diplomarbeit]

  • Doctor (Dr.), Technische Universiteit Eindhoven, 2008     [Proefschrift]


Erdös-Bacon number 6 (=3+3)