Prof. Dr. Marc Ke?eb?hmer

Preprints

1. Denker, Manfred; Kesseb?hmer, Marc; Lopes, Artur O.; Lopes, Silvia R.C.
   Parametrized Families of Gibbs Measures and their Statistical Inference
   arXiv: 2408.01104.
    
2. Kesseb?hmer, Marc; Niemann, Aljoscha
   Quantization dimensions of negative order
   arXiv: 2405.1338.
    
3. Breitkopf, Laura; Kesseb?hmer, Marc; Pohl, Anke
   Equidistribution of cusp points of Hecke triangle groups
   arXiv: 2402.04784.
    
4. Kesseb?hmer, Marc; Niemann, Aljoscha 
   Exact asymptotic order for generalised adaptive approximations
   arXiv: 2312.16644.
    
5. Kesseb?hmer, Marc; Wiegmann, Linus
   Approximation order of Kolmogorov, Gel'fand, and linear widths for Sobolev embeddings in euclidian measure spaces
   arXiv: 2303.01320.
    
6. Kesseb?hmer, Marc; Niemann, Aljoscha
   Spectral dimensions of Krein-Feller operators in higher dimensions
   arXiv:  2202.05247.
    
7. Schünemann, Maik; Ernst, Udo; Kesseb?hmer, Marc
   A rigorous stochastic theory for spike pattern formation in recurrent neural networks with arbitrary connection topologies
   arXiv: 2202.02520.
    

8. Kesseb?hmer, Marc; Kombrink, Sabrina.
   Minkowski measurability of infinite conformal graph directed systems and application to Apollonian packings.
   arXiv: 1702.02854.

Published Articles

1. Kesseb?hmer, Marc; Niemann, Aljoscha; Samuel, Tony; Weyer, Hendrik.
   Generalised  Kre?n—Feller operators and gap diffusions via transformations of measure spaces.
   To appear in: "From Classical Analysis to Analysis on Fractals. A Tribute to Robert Strichartz, Volume 2", Applied and Numerical Harmonic Analysis, Birkh?user, 2024. 
   arXiv: 1909.08832.
    
2. Kesseb?hmer, Marc; Niemannn, Aljoscha; Zhu, Sanguo
   Quantization dimensions of compactly supported probability measures via Rényi dimensions
   Trans. Amer. Math. Soc. 376 (2023), pp. 4661-4678.
   DOI: 10.1090/tran/8863. arXiv: 2205.15776.
    
3. Kesseb?hmer, Marc; Niemann, Aljoscha
   Approximation order of Kolmogorov diameters via L^q-spectra and applications to polyharmonic operators.
   Journal of Functional Analysis, Volume 282, Issue 9, 2022, Article 109598, ISSN 0022-1236
   DOI: 10.1016/j.jfa.2022.109598. arXiv: 2107.07932.
    
4. Kesseb?hmer, Marc; Niemann, Aljoscha
   Spectral asymptotics of Kre?n-Feller operators for weak Gibbs measures on self-conformal fractals with overlaps
   Advances in Mathematics, Volume 403, 2022, Paper No. 108384, ISSN 0001-8708.
   DOI: 10.1016/j.aim.2022.108384. arXiv: 2107.02616.
    
5. Kesseb?hmer, Marc; Niemann, Aljoscha.
   Spectral dimensions of Kre?n-Feller operators and Lq-spectra.
   Advances in Mathematics, Volume 399, 2022.
   DOI: 10.1016/j.aim.2022.108253. arXiv: 2106.08862.
    
6. Gr?ger, Maik; Jaerisch, Johannes; Kesseb?hmer, Marc.
   Thermodynamic formalism for transient dynamics on the real line.
   Nonlinearity 35, 1093–1118  (2022).
   DOI: 10.1088/1361-6544/ac45ea. arXiv: 1905.09077.
    
7. Jaerisch, Johannes; Kesseb?hmer, Marc; Munday, Sara.
   A multifractal analysis for cuspidal windings on hyperbolic surfaces.
   Stochastics and Dynamics Vol. 21, No. 03, 2140007 (2021).
   DOI: 10.1142/S0219493721400074. arXiv: 1610.05827.
    
8. Kesseb?hmer, Marc; Schindler, Tanja.
   Mean convergence for intermediately trimmed Birkhoff sums of observables with regularly varying tails.
   Nonlinearity 33(10), 5543?–5566 (2020). 
   DOI: 10.1088/1361-6544/ab9585. arXiv: 1903.09337.
    
9. Kesseb?hmer, Marc; Samuel, Tony; Weyer, Hendrik.
   Measure-geometric Laplacians for partially atomic measures.
   Comment. Math. Univ. Carolin. 61, 313-335 (2020).
   DOI: 10.14712/1213-7243.2020.026
   Title of preprint: Measure-geometric Laplacians on the real line. arXiv: 1802.04858.
    
10. Kesseb?hmer, Marc; Rademacher, Jens; Ulbrich, Dennis.
    Dynamics and topological entropy of 1D Greenberg-Hastings cellular automata.
    Ergodic Theory and Dynamical Systems, 41 (2020), no. 5, 1397–1430.
    DOI:10.1017/etds.2020.18. arXiv: 1903.02459.
     
11. Kesseb?hmer, Marc; Schindler, Tanja.
    Limit theorems for counting large continued fraction digits.
    Lith Math J 60, 189–207 (2020). 
    DOI:10.1007/s10986-020-09479-5. arXiv: 1604.06612.
     
12. Kesseb?hmer, Marc; Samuel, Tony; Sender, Karenina.
    The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain.
    J. Fractal Geom.7, 113?–136 (2020).
    DOI: 10.4171/JFG/86. arXiv: 1710.04414.
     
13. Kesseb?hmer, Marc; Schindler, Tanja.
    Intermediately trimmed strong laws for Birkhoff sums on subshifts of finite type.
    Dynamical Systems. An International Journal 35(2): 275?–305 (2020).
    DOI: 10.1080/14689367.2019.1667305. arXiv: 1901.04478.
     
14. Baake, Michael; Gohlke, Philipp; Kesseb?hmer, Marc; Schindler, Tanja.
    Scaling properties of the Thue--Morse measure.
    Discrete Contin. Dyn. Syst. Ser. A, 39(7): 4157?–4185 (2019).
    DOI: 10.3934/dcds.2019168. arXiv: 1810.06949.
     
15. Kesseb?hmer, Marc; Mosbach, Arne; Samuel, Tony; Steffens, Malte.
    Diffraction of return time measures.
    J. Stat. Phys. 174(3): 519?–535 (2019).
    DOI: 10.1007/s10955-018-2196-5. arXiv:1801.07608.
     
16. Kesseb?hmer, Marc; Schindler, Tanja.
    Strong laws of large number for intermediately trimmed Birkhoff sums of observables with infinite mean.
    Stochastic Processes and their Applications 129(10): 4163?–4207 (2019).
    DOI: 10.1016/j.spa.2018.11.015. arXiv: 1706.07369.
     
17. Kesseb?hmer, Marc; Samuel, Tony; Weyer, Hendrik.
    Measure-geometric Laplacians for discrete distributions.
    In Niemeyer et al., editor, Horizons of Fractal Geometry and Complex Dimensions, volume 731 of Contemp. Math., pages 133–142. Amer. Math. Soc., Providence, R.I. (2019). 
    DOI: 10.1090/conm/731/14676. arXiv: 1702.03873.
     
18. Dreher, Fabian; Kesseb?hmer, Marc.
    Escape rates for special flows and their higher order asymptotics.
    Ergod. Th. & Dynam. Sys.39: 1501–1530 (2019).
    DOI: 10.1017/etds.2017.76. arXiv: 1605.00467.
     
19. Kesseb?hmer, Marc; Schindler, Tanja.
    Strong laws of large numbers for intermediately trimmed sums of i.i.d. random variables with infinite mean.
    J.Theor. Probab., 32(2): 702?–720 (2019).
    DOI: 10.1007/s10959-017-0802-0. arXiv: 1609.04910.
     
20. Gr?ger, Maik; Kesseb?hmer, Marc; Mosbach, Arne; Samuel, Tony; Steffens, Malte.
    A classification of aperiodic order via spectral metrics and Jarník sets.
    Ergodic Theory and Dynamical Systems, 39(11): 3031?–3065 (2019).
    DOI: 10.1017/etds.2018.7 arXiv: 1601.06435.
     
21. Dreher, Fabian; Kesseb?hmer, Marc; Mosbach, Arne; Samuel, Tony; Steffens, Malte.
    Regularity of aperiodic minimal subshifts.
    Bull. Math. Sci.  8: 413?–434 (2018).
    DOI: 10.1007/s13373-017-0102-0. arXiv: 1610.03163.
     
22. Kesseb?hmer, Marc; Kombrink, Sabrina.
    A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory.
    Discrete and Continuous Dynamical Systems - Series S , 10(2): 335?–352 (2017).
    DOI: 10.3934/dcdss.2017016. arViv: 1604.08252.
     
23. Kesseb?hmer, Marc; Zhu, Sanguo.
    The upper and lower quantization coefficient for Markov-type measures.
    Mathematische Nachrichten 290(5-6): 827?–839 (2017).
    DOI:10.1002/mana.201500328
    Title of preprint: The quantization for Markov-type measures on a class of ratio-specified graph directed fractals. arXiv:1406.3257.
     
24. Kesseb?hmer, Marc; Samuel, Tony; Weyer, Hendrik.
    A note on measure-geometric Laplacians. 
    Monatshefte für Mathematik 181: 643?–655 (2016). 
    DOI: 10.1007/s00605-016-0906-0. arXiv: 1411.2491.
     
25. Kautzsch, Johannes; Kesseb?hmer, Marc; Samuel, Tony. 
    On the convergence to equilibrium of unbounded observables under a family of intermittent interval maps. 
    Ann. Henri Poincaré  17(9): 2585?–2621(2016).
    DOI:10.1007/s00023-015-0451-8. arXiv: 1410.3805.
     
26. Kesseb?hmer, Marc; Zhu, Sanguo.
    Some recent developments in quantization of fractal measures.
    Fractal geometry and stochastics V, Progr. Probab. 70: 105?–120 (2015).
    DOI:10.1007/978-3-319-18660-3_7. arXiv: 1501.04814.
     
27. Kautzsch, Johannes; Kesseb?hmer, Marc; Samuel, Tony; Stratmann, Bernd O.
    On the asymptotics of the α-Farey transfer operator. 
    Nonlinearity 28: 143?–166 (2015).
    DOI: 10.1088/0951-7715/28/1/143. arXiv:1404.5857. 
     
28. Kesseb?hmer, Marc; Zhu, Sanguo.
    On the quantization for self-affine measures on Bedford-McMullen carpets. 
    Mathematische Zeitschrift  283(1): 39?–58 (2015).
    DOI: 10.1007/s00209-015-1588-3. arXiv:1312.3289.
     
29. Kesseb?hmer, Marc; Kombrink, Sabrina.
    Minkowski content and fractal Euler characteristic for conformal graph directed systems.
    Journal of Fractal Geometry 2: 171–227 (2015).
    DOI:10.4171/JFG/19. arXiv: 1211.733.
     
30. Jaerisch, Johannes; Kesseb?hmer, Marc; Lamei, Sanaz.  
    Induced topological pressure for countable state Markov shifts. 
    Stoch. Dyn. 14 (2), (2014).
    DOI: 10.1142/S0219493713500160. arXiv: 1010.2162.
     
31. Jaerisch, Johannes; Kesseb?hmer, Marc; Stratmann, Bernd O.
    A Fréchet law and an Erd?s-Philipp law for maximal cuspidal windings. 
    Ergodic Theory Dynam. Systems 33 (4): 1008–1028 (2013).
    DOI: 10.1017/S0143385712000235. arXiv: 1109.3583.
     
32. Kesseb?hmer, Marc; Samuel, Tony.
    Spectral metric spaces for Gibbs measures. 
    J. Funct. Anal. 265 (9): 1801?–1828 (2013). 
    DOI: 10.1016/j.jfa.2013.07.012. arXiv: 1012.5152.
     
33. Bohnstengel, Jana; Kesseb?hmer, Marc.
    Multiresolution analysis for Markov Interval Maps. 
    Numer. Funct. Anal. and Optim. 33 (7-9): 791?–832 (2012). 
    DOI: 10.1080/01630563.2012.682126. arXiv: 1107.0275.
     
34. Kesseb?hmer, Marc; Kombrink, Sabrina.
    Fractal curvature measures and Minkowski content for self-conformal subsets of the real line. 
    Advances in Mathematics 230: 2474?–2512 (2012). 
    DOI: 10.1016/j.aim.2012.04.023.
    Title of preprint: Fractal curvature measures and Minkowski content for one-dimensional self-conformal sets. arXiv: 1012.5399.
     
35. Kesseb?hmer, Marc; Stratmann, Bernd.
    A dichotomy between uniform distributions of the Stern-Brocot and the Farey sequence.
    Unif. Distrib. Theory 7 (2): 21–33 (2012).
    arXiv: 1009.1823.  PDF
     
36. Kesseb?hmer, Marc; Munday, Sara; Stratmann, Bernd O.
    Strong renewal theorems and Lyapunov spectra for α-Farey and α-Lüroth systems.
    Ergodic Theory Dynam. Systems 32 (3): 989?–1017(2012).
    DOI: 10.1017/S0143385711000186. arXiv:1006.5693.
     
37. Kesseb?hmer, Marc; Stratmann, Bernd O.
    A note on the algebraic growth rate of Poincaré series for Kleinian groups.
    Contributions in analytic and algebraic number theory, Springer Proc. Math., 9, Springer, New York, 237–245 (2012).
    DOI: 10.1007/978-1-4614-1219-9_10. arXiv:0910.5560.
     
38. Kesseb?hmer, Marc; Stratmann, Bernd O.
    On the asymptotic behaviour of the Lebesgue measure of sum-level sets for continued fractions.
    Discrete Contin. Dyn. Syst. 32 (7): 2437?–2451(2012).
    DOI: 10.3934/dcds.2012.32.2437.
    Title of preprint: On the Lebesgue measure of sum-level sets for continued fractions. arXiv: 0901.1787.
     
39. Jaerisch, Johannes; Kesseb?hmer, Marc.
    Regularity of multifractal spectra of conformal iterated function systems.
    Trans. Amer. Math. Soc. 363 (1): 313–330 (2011).
    DOI: 10.1007/s11512-009-0102-8. arXiv: 0902.2473.
     
40. Bohnstengel, Jana; Kesseb?hmer, Marc.
    Wavelets for iterated function systems.
    J. Funct. Anal. 259 (3): 583–601 (2010).
    DOI: 10.1016/j.jfa.2010.04.014. arXiv: 0910.0609.
     
41. Jaerisch, Johannes; Kesseb?hmer, Marc.
    The arithmetic-geometric scaling spectrum for continued fractions. 
    Ark. Mat. 48 (2): 335–360 (2010).
    DOI: 10.1007/s11512-009-0102-8. arXiv: 0808.2308.
     
42. Jordan, Thomas; Kesseb?hmer, Marc; Pollicott, Mark; Stratmann, Bernd O.
    Sets of nondifferentiability for conjugacies between expanding interval maps. 
    Fund. Math. 206: 161–183 (2009).
    DOI: 10.4064/fm206-0-10. arXiv: 0807.0115.
     
43. Kesseb?hmer, Marc; Stratmann, Bernd O.
    H?lder-differentiability of Gibbs distribution functions. 
    Math. Proc. Cambridge Philos. Soc. 147 (2): 489–503 (2009).
    DOI: 10.1017/S0305004109002473. arXiv: 0711.4698.
     
44. Kesseb?hmer, Marc; Stratmann, Bernd O.
    Fractal analysis for sets of non-differentiability of Minkowski's question mark function. 
    J. Number Theory 128 (9): 2663?–2686 (2008).
    DOI: 10.1016/j.jnt.2007.12.010. arXiv: 0706.0453.
     
45. Kesseb?hmer, Marc; Slassi, Mehdi.
    Large deviation asymptotics for continued fraction expansions. 
    Stoch. Dyn. 8 (1): 103–113 (2008).
    DOI: 10.1142/S0219493708002226. arXiv: 0702381.
     
46. Kesseb?hmer, Marc; Stratmann, Bernd O.
    Refined measurable rigidity and flexibility for conformal iterated function systems. 
    New York J. Math. 14: 33–51 (2008).
    arXiv: 0603571.
     
47. Kesseb?hmer, Marc; Slassi, Mehdi.
    A distributional limit law for the continued fraction digit sum. 
    Math. Nachr. 281 (9): 1294–1306 (2008).
    DOI: 10.1002/mana.200510679. arXiv: 0509559.
     
48. Kesseb?hmer, Marc; Urbański, Mariusz.
    Higher-dimensional multifractal value sets for conformal infinite graph directed Markov systems. 
    Nonlinearity 20 (8): 1969–1985 (2007).
    DOI: 10.1088/0951-7715/20/8/009. arXiv: 0701541.
     
49. Kesseb?hmer, M.; Stratmann, B. O.
    Homology at infinity; fractal geometry of limiting symbols for modular subgroups. 
    Topology 46 (5): 469–491 (2007).
    DOI: 10.1016/j.top.2007.03.004.
    Title of preprint: Limiting modular symbols and their fractal geometry. arXiv: 0611048.
     
50. Kesseb?hmer, Marc; Slassi, Mehdi.
    Limit laws for distorted critical return time processes in infinite ergodic theory. 
    Stoch. Dyn. 7 (1): 103–121 (2007).
    DOI: 10.1142/S0219493707001962.
    Title of preprint: Critical waiting time processes in infinite ergodic theory. arXiv: 0607681.
     
51. Kesseb?hmer, Marc; Stadlbauer, Manuel; Stratmann, Bernd O.
    Lyapunov spectra for KMS states on Cuntz-Krieger algebras. 
    Math. Z. 256 (4): 871–893 (2007).
    DOI: 10.1007/s00209-007-0110-y.
    Title of preprint: Radon--Nikodym representations of Cuntz--Krieger algebras and Lyapunov spectra for KMS states. arXiv: 0601354.
     
52. Kesseb?hmer, Marc ; Stratmann, Bernd O.
    A multifractal analysis for Stern-Brocot intervals, continued fractions and Diophantine growth rates.
    J. Reine Angew. Math. 605: 133?–163 (2007).
    DOI: 10.1515/CRELLE.2007.029. arXiv: 0509603.
     
53. Kesseb?hmer, Marc ; Zhu, Sanguo.
    Stability of quantization dimension and quantization for homogeneous Cantor measures.
    Math. Nachr. 280 (8): 866?–881 (2007).
    DOI: 10.1002/mana.200410519.
     
54. Kesseb?hmer, Marc ; Zhu, Sanguo.
    Dimension sets for infinite IFSs: the Texan conjecture.
    J. Number Theory 116 (1): 230?–246 (2006).
    DOI:10.1016/j.jnt.2005.04.002.
     
55. Kesseb?hmer, Marc ; Stratmann, Bernd O.
    Stern-Brocot pressure and multifractal spectra in ergodic theory of numbers.
    Stoch. Dyn. 4 (1): 77?–84 (2004).
    DOI: 10.1142/S0219493704000948.
     
56. Kesseb?hmer, Marc ; Stratmann, Bernd O.
    A multifractal formalism for growth rates and applications to geometrically finite Kleinian groups.
    Ergodic Theory Dynam. Systems 24 (1): 141?–170 (2004).
    DOI: 10.1017/S0143385703000282.
     
57. Kesseb?hmer, Marc ; Zhu, Sanguo .
    Quantization dimension via quantization numbers.
    Real Anal. Exchange 29 (2): 857?–866 (2003).
    http://projecteuclid.org/euclid.rae/1149698548.
     
58. Denker, Manfred ; Kesseb?hmer, Marc.
    Thermodynamic formalism, large deviation, and multifractals.
    Stochastic climate models (Chorin, 1999), 159?–169, Progr. Probab., 49, Birkh?user, Basel (2001).
    DOI: 10.1007/978-3-0348-8287-3_6.
     
59. Kesseb?hmer, Marc .
    Large deviation for weak Gibbs measures and multifractal spectra.
    Nonlinearity 14 (2): 395?–409 (2001).
    DOI: 10.1088/0951-7715/14/2/312.

Books

1. Kesseb?hmer, Marc; Munday, Sara; Stratmann, Bernd.
   Infinite Ergodic Theory of Numbers.
   De Gruyter Textbook, 191 pages (2016).
   ISBN: 978-3-11-043942-7.

Editor:

1. Preface: Thermodynamic formalism - Applications to geometry, number theory, and stochastics.
   Stochastics and Dynamics Vol. 21, No. 03, 2102001 (2021).
   M. Kesseb?hmer, S. Kombrink, Y. Pesin, T. Samuel and J. Schmeling.
   DOI: 10.1142/S0219493721020019
    
2. Preface: Diffusion on fractals and non-linear dynamics. 
   Discrete Contin. Dyn. Syst. Ser. S 10(2), 2017.
   K. Falk, T. J?ger, M. Kesseb?hmer, J. Rademacher and T. Samuel.
   DOI: 10.3934/dcdss.201702i