Department Mathematik



Markus Heydenreich


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 2021/22)

Student seminar: Circle packings and random walks with S. Hensel (winter term 2021/22)

Student seminar: Zufall und Simulation (LA Gym und WiPäd) with S. Ufer (winter term 2021/22)

Stochastik für Lehramtsstudierende (summer term 2021)

Reading seminar: Interacting Particle Systems (summer term 2021)

Oberseminar: Mathematical Epidemiology: Modelling and Inference (summer term 2021)

Research seminars in Munich

Oberseminar Wahrscheinlichkeitstheorie organized jointly with TUM

Mathematical Colloquium at LMU Munich

Augsburg-Munich Day on Exclusion Processes at LMU Munich on 17 December 2021


I am a mathematician; my field of expertise is probability theory. I am studying discrete random objects of varying flavour, such as
  • phase transitions in models of statistical mechanics, mean-field behaviour, lace expansion;
  • long-range order of discrete models in continuum space, symmetry breaking, crystallization;
  • spatial random graph models;
  • random walk in dynamic random environment.

Current projects

Further activities

Office hour

Please make appointments via email.

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



  • M. Heydenreich and R. van der Hofstad,
    Progress in high-dimensional percolation and random graphs (xii+285 pages).
    CRM Short Courses, Springer (2017).
    []   [pdf]



    I make preprints available via [my-preprints@arXiv]

  • N. Hao and M. Heydenreich,
    Graph distances in scale-free percolation: the logarithmic case.
    Preprint, 20 pages.
  • A. Drewitz, M. Heydenreich, and C. Mailler,
    Voronoi cells in random split trees.
    Preprint, 25 pages.
  • P. Gracar, M. Heydenreich, C. Mönch, and P. Mörters,
    Recurrence versus transience for weight-dependent random connection models.
    Preprint, 32 pages.
  • M. Heydenreich, R. van der Hofstad, G. Last, and K. Matzke,
    Lace Expansion and Mean-Field Behavior for the Random Connection Model.
    Preprint, 62 pages.

Published articles

  • D. Conache, M. Heydenreich, F. Merkl, and S.W.W. Rolles,
    Variance of voltages in a lattice Coulomb gas.
    Journal of Statistical Physics 186(1):16pp (2022).
    [article@SpringerLink]  [preprint@arXiv]
  • M. Heydenreich and C. Hirsch,
    Extremal linkage networks.
    Extremes, OnlineFirst (2021).
    [article@SpringerLink]  [preprint@arXiv]
  • M. Heydenreich and K. Matzke,
    Expansion for the critical point of site percolation: the first three terms.
    Combinatorics, Probability and Computing, FirstView (2021).
    [article@CambridgeCore]   [preprint@arXiv]
  • M. Heydenreich,
    Fractal dimension of discrete sets and percolation.
    In: Freiberg U., Hambly B., Hinz M., Winter S. (eds) Fractal Geometry and Stochastics VI.
    Progress in Probability, vol. 76, pp. 101-124. Birkhäuser, Cham (2021).
    [article@SpringerLink]   [preprint@arXiv]
  • M. Heydenreich and K. Matzke,
    Critical site percolation in high dimension.
    Journal of Statistical Physics 181(3):816-853 (2020).
    [article@SpringerLink] (open access)  
  • N. Gantert, M. Heydenreich, and T. Hirscher,
    Strictly weak consensus in the uniform compass model on ℤ.
    Bernoulli 26(2):1269-1293 (2020).
    [article@ProjectEuclid]   [preprint@arXiv]  
  • S. Handa, M. Heydenreich, and A. Sakai,
    Mean-field bound on the 1-arm exponent for Ising ferromagnets in high dimensions.
    In: Sidoravicius V. (eds) Sojourns in Probability Theory and Statistical Physics - I.
    Springer Proceedings in Mathematics & Statistics, vol. 298, pp. 183–198 (2019).
    [article@SpringerLink]   [preprint@arXiv]
  • R. Bauerschmidt, D. Conache, M. Heydenreich, F. Merkl, S.W.W. Rolles,
    Dislocation lines in three-dimensional solids at low temperature.
    Annales Henri Poincaré 20(9):3019–3057 (2019).
    [article@SpringerLink] (open access)  
  • M. Gottschau, M. Heydenreich, K. Matzke, and C. Toninelli,
    Phase transition for a non-attractive infection process in heterogeneous environment.
    Markov Processeses and Related Fields 24(1):39-56 (2018).
    [article@MPRF]   [preprint@arXiv]
  • M. Heydenreich, C. Hirsch, D. Valesin,
    Uniformity of hitting times for the contact process.
    ALEA, Latin American Journal of Probability and Mathematical Statistics 15: 233–245 (2018).
    [article@ALEA](open access) 
  • M. Heydenreich, L. Kolesnikov,
    The critical 1-arm exponent for the ferromagnetic Ising model on the Bethe lattice
    Journal of Mathematical Physics 59, 043301 (2018).
    [article@AIP]   [preprint@arXiv]
  • M. Heydenreich, T. Hulshof, and J. Jorritsma,
    Structures in supercritical scale-free percolation.
    Annals of Applied Probability 27(4):2569-2604 (2017).
    [article@ProjectEuclid]   [preprint@arXiv]
  • S. Bethuelsen and M. Heydenreich,
    Random Walks on Attractive Spin-Flip Dynamics: Law of Large Numbers and Large Deviation Estimates.
    Stochastic Processes and Applications 127(7):2346-2372 (2017).
    [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@ProjectEuclid]   [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).
    Erratum: Probability Theory and Related Fields 175 (3-4): 1183-1185 (2019).
    [article@SpringerLink] (open access)   [erratum@SpringerLink]    [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)  
  • 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.

  • P. Gracar, M. Heydenreich, C. Mönch, and P. Mörters,
    Transience Versus Recurrence for Scale-Free Spatial Networks. In: Kamiński B., Prałat P., Szufel P. (eds) Algorithms and Models for the Web Graph. WAW 2020. Lecture Notes in Computer Science, vol 12091. Springer, Cham (2020).
  • M. Heydenreich and C. Hirsch,
    A Spatial Small-World Graph Arising from Activity-Based Reinforcement. In: Avrachenkov K., Prałat P., Ye N. (eds) Algorithms and Models for the Web Graph. WAW 2019. LNCS 11631, pp. 102–114. Springer, Cham (2019).
    [proceedings@SpringerLink]   [preprint@arXiv]
  • 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.

Editorial work

  • Adams, Stefan; Baake, Michael; Heydenreich, Markus,
    Mini-workshop: Mathematics of Crystallisation.
    Oberwolfach Reports 16 (2):1071-1111 (2019).
  • 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.

Organization of conferences and workshops

MATRIX-MFO Tandom Workshop Stochastic Reinforcement Processes and Graphs at Mathematisches Forschungsinstitut Oberwolfach (Germany) and MATRIX at Creswick (Australia), March 5-11, 2023. Jointly organized with Cécile Mailler (Bath), Viktor Kleptsyn (Rennes), and Mark Holmes (Melbourne).
[Workshop website]
Workshop Graph limits and random walks at Benediktbeuern (September 13-16, 2020) as part of DFG Scientific Network Stochastic Processes on Evolving Networks
[Workshop website]
Workshop Random Walk, Random Graphs and Random Media in Munich, September 9-13, 2019. Jointly organized with Noam Berger (TUM), Alexander Drewitz (Cologne), Nina Gantert (TUM), and Alejandro Ramirez (Santiago).
[Workshop website]

Mini-Workshop Mathematics of Crystallization at Mathematisches Forschungsinstitut Oberwolfach, April 7-13, 2019. Jointly organized with Stefan Adams (Warwick) and Michael Baake (Bielefeld).
[Workshop website]
Workshop Random Structures in Neurosciences and Biology,
held in Herrsching, March 26-29, 2018.
Jointly organized with Christian Hirsch (LMU)
[Workshop website

Probability Day Erlangen-München, joint annual event of FAU Erlangen-Nürnberg, TU München and LMU München.
[2016]  [2017]  [2018]  [2019] [2020]
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]


  • Diplom-Wirtschaftsmathematik (dipl. math. oec.), Technische Universität Berlin, 2004     [Diplomarbeit]
  • Doctor (Dr.), Technische Universiteit Eindhoven, 2008     [Proefschrift]