Publications of Markus Heydenreich

Book

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

Preprints

    I make preprints available via arxiv.org [my-preprints@arXiv]

• M. Dickson and M. Heydenreich,
  The Triangle Condition for the Marked Random Connection Model.
  Preprint, 85 pages.
  [preprint@arXiv]
• M. Heydenreich, L. Taggi, and N. Torri,
  Prudent walk in dimension six and higher.
  Preprint, 33 pages.
  [preprint@arXiv]
• A. Drewitz, M. Heydenreich, and C. Mailler,
  Voronoi cells in random split trees.
  Preprint, 25 pages.
  [preprint@arXiv]
• 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.
  [preprint@arXiv]

Published articles

• N. Hao and M. Heydenreich,
  Graph distances in scale-free percolation: the logarithmic case.
  Journal of Applied Probability (FirstView).
  [article@CambridgeCore]   [preprint@arXiv]
• P. Gracar, M. Heydenreich, C. Mönch, and P. Mörters,
  Recurrence versus transience for weight-dependent random connection models.
  Electronic Journal of Probability 27, paper no. 60:31pp (2022).
  [paper@ProjectEuclid]  (open access)
• 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]  (open access)
• M. Heydenreich and C. Hirsch,
  Extremal linkage networks.
  Extremes 25(2):229–255 (2022).
  [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 31(3):430-454 (2022).
  [article@CambridgeCore]  (open access)
• 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). 
  [article@IEEE-Xplore]
  
• 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).
  [proceedings@SpringerLink]
• 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.
  [pdf]

Editorial work

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