Marco Lenci: Research Page


Brief Curriculum Vitae

Scientific interests

Dynamical systems, ergodic theory, probability theory, applications to physical systems (diffusion, transport, etc.), statistical mechanics.

Publications

Research

  1. Limit theorems and lack thereof for a multilayer random walk mimicking human mobility (with A. Bianchi & F. Pène), preprint (2025)
    [    arXiv:2503.01503]
  2. Uniformly global observables for 1D maps with an indifferent fixed point (with G. Canestrari), preprint (2024)
    [arXiv:2405.05948]
  3. Preface [to the special issue "Advances in Dynamical Systems by the DinAmicI group"] (with C. Bonanno), Boll. Unione Mat. Ital. 16 (2023), no. 2, 151-152
    [DOI: 10.1007/s40574-023-00366-8]
  4. Discrete- and continuous-time random walks in 1D Lévy random medium, in: P. Barbante et al. (eds.), From Kinetic Theory to Turbulence Modeling: The Legacy of Carlo Cercignani, Springer INdAM Series 51, 2023
    [DOI: 10.1007/978-981-19-6462-6_13 | arXiv:2112.08822]
  5. Internal-wave billiards in trapezoids and similar tables (with C. Bonanno & G. Cristadoro), Nonlinearity 36 (2023), no. 2, 1029-1052
    [DOI: 10.1088/1361-6544/ac98ef | arXiv:2102.01654]
  6. Extensions of exact and K-mixing dynamical systems (with D. Galli), J. Stat. Phys. 190 (2023), no. 1, Paper No. 21, 15 pp.
    [DOI: 10.1007/s10955-022-03039-6 | arXiv:2203.11822]
  7. Maximal escape rate for shifts (with C. Bonanno & G. Cristadoro), Discrete Contin. Dyn. Syst. 42 (2022), no. 12, 6007-6029
    [DOI: 10.3934/dcds.2022135 | arXiv:2112.14248]
  8. Limit theorems for Lévy flights on a 1D Lévy random medium (with G. Bet, A. Bianchi, E. Magnanini & S. Stivanello), Electron. J. Probab. 26 (2021), article no. 57, 1-25
    [DOI: 10.1214/21-EJP626 | arXiv:2007.03384]
  9. Global observables for RW: law of large numbers (with D. Dolgopyat & P. Nándori), Ann. Inst. Henri Poincaré Probab. Stat. 57 (2021), no. 1, 94-115
    [DOI: 10.1214/20-AIHP1072 | arXiv:1902.11071]
  10. Pomeau-Manneville maps are global-local mixing (with C. Bonanno), Discrete Contin. Dyn. Syst. 41 (2021), no. 3, 1051-1069
    [DOI: 10.3934/dcds.2020309 | arXiv:1911.02913]
  11. Continuous-time random walk between Lévy-spaced targets in the real line (with A. Bianchi & F. Pène), Stochastic Process. Appl. 130 (2020), no. 2, 708-732
    [DOI: 10.1016/j.spa.2019.03.010 | arXiv:1806.02278]
  12. Infinite mixing for one-dimensional maps with an indifferent fixed point (with C. Bonanno & P. Giulietti), Nonlinearity 31 (2018), no. 11, 5180-5213
    [DOI: 10.1088/1361-6544/aadc04 | arXiv:1708.09369]
  13. Pointwise convergence of Birkhoff averages for global observables (with S. Munday), Chaos 28 (2018), 083111, 16 pp.
    [DOI: 10.1063/1.5036652 | arXiv:1804.05359]
  14. Global-local mixing for the Boole map (with C. Bonanno & P. Giulietti), Chaos Solitons Fractals 111 (2018), 55-61
    [DOI: 10.1016/j.chaos.2018.03.020 | arXiv:1802.00397]
  15. Uniformly expanding Markov maps of the real line: exactness and infinite mixing, Discrete Contin. Dyn. Syst. 37 (2017), no. 7, 3867-3903
    [DOI: 10.3934/dcds.2017163 | arXiv:1404.2212]
  16. Random walks in a one-dimensional Lévy random environment (with A. Bianchi, G. Cristadoro & M. Ligabò), J. Stat. Phys. 163 (2016), no. 1, 22-40
    [DOI: 10.1007/s10955-016-1469-0 | arXiv:1411.0586]
  17. Characterization of DNA methylation as a function of biological complexity via dinucleotide inter-distances (with G. Paci, G. Cristadoro, B. Monti, M. Degli Esposti, G. C. Castellani & D. Remondini), Phil. Trans. R. Soc. A (2016) 20150227, 11 pp.
    [DOI: 10.1098/rsta.2015.0227 | arXiv:1511.08445]
  18. A simple proof of the exactness of expanding maps of the interval with an indifferent fixed point, Chaos Solitons Fractals 82 (2016), 148-154
    [DOI: 10.1016/j.chaos.2015.11.024 | arXiv:1511.05906]
  19. Lévy walks on lattices as multi-state processes (with G. Cristadoro, T. Gilbert & D. P. Sanders), J. Stat. Mech. (2015), P05012, 25 pp.
    [DOI: 10.1088/1742-5468/2015/05/P05012 | arXiv:1501.05216]
  20. Transport properties of Lévy walks: an analysis in terms of multistate processes (with G. Cristadoro, T. Gilbert & D. P. Sanders), Europhys. Lett. 108 (2014), no. 5, 50002, 6 pp.
    [DOI: 10.1209/0295-5075/108/50002 | arXiv:1407.0227]
  21. Machta-Zwanzig regime of anomalous diffusion in infinite-horizon billiards (with G. Cristadoro, T. Gilbert & D. P. Sanders), Phys. Rev. E 90 (2014), 050102(R), 5 pp.
    [DOI: 10.1103/PhysRevE.90.050102 | arXiv:1408.0349]
  22. Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards (with G. Cristadoro, T. Gilbert & D. P. Sanders), Phys. Rev. E 90 (2014), 022106, 10 pp.
    [DOI: 10.1103/PhysRevE.90.022106 | arXiv:1405.0975]
  23. Exactness, K-property and infinite mixing, Publ. Mat. Urug. 14 (2013), 159-170
    [link to issue | arXiv:1212.4099]
  24. Random walks in random environments without ellipticity, Stochastic Process. Appl. 123 (2013), no. 5, 1750-1764
    [DOI: 10.1016/j.spa.2013.01.007 | arXiv:1106.6008]
  25. Infinite-volume mixing for dynamical systems preserving an infinite measure, Procedia IUTAM 5 (2012), 204-219
    [DOI: 10.1016/j.piutam.2012.06.028 | arXiv:1202.6391]
  26. Infinite-horizon Lorentz tubes and gases: recurrence and ergodic properties (with S. Troubetzkoy), Physica D 240 (2011), no. 19, 1510-1515
    [DOI: 10.1016/j.physd.2011.06.020 | arXiv:1103.6110]
  27. Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two (with M. Seri, M. Degli Esposti & G. Cristadoro), J. Stat. Phys. 144 (2011), no. 1, 124-138
    [DOI: 10.1007/s10955-011-0244-5 | arXiv:1011.6414]
  28. Recurrence for quenched random Lorentz tubes (with G. Cristadoro & M. Seri), Chaos 20 (2010), 023115, 7 pp.; erratum at Chaos 20 (2010), 049903, 1 p.
    [DOI: 10.1063/1.3405290 | arXiv:0909.3069]
  29. On infinite-volume mixing, Comm. Math. Phys. 298 (2010), no. 2, 485-514
    [DOI: 10.1007/s00220-010-1043-6 | arXiv:0906.4059]
  30. Central Limit Theorem and recurrence for random walks in bistochastic random environments, J. Math. Phys. 49 (2008), no. 12, 125213, 9 pp.
    [DOI: 10.1063/1.3005226 | arXiv:0810.2324]
  31. Hyperbolic billiards with nearly flat focusing boundaries. I (with L. Bussolari), Physica D 237 (2008), no. 18, 2272-2281
    [DOI: 10.1016/j.physd.2008.02.006 | arXiv:0712.3802]
  32. Recurrence for persistent random walks in two dimensions, Stoch. Dyn. 7 (2007), no. 1, 53-74
    [DOI: 10.1142/S0219493707001937 | arXiv:math/0507411]
  33. Typicality of recurrence for Lorentz gases, Ergodic Theory Dynam. Systems 26 (2006), no. 3, 799-820
    [DOI: 10.1017/S0143385706000022 | arXiv:math/0410355]
  34. Large deviations in quantum lattice systems: one-phase region (with L. Rey-Bellet), J. Stat. Phys. 119 (2005), no. 3-4, 715-746
    [DOI: 10.1007/s10955-005-3015-3 | arXiv:math-ph/0406065]
  35. Localization in infinite billiards: a comparison between quantum and classical ergodicity (with S. Graffi), J. Statist. Phys. 116 (2004), no. 1-4, 821-830
    [DOI: 10.1023/B:JOSS.0000037218.05161.f3 | arXiv:math-ph/0306075]
  36. Aperiodic Lorentz gas: recurrence and ergodicity, Ergodic Theory Dynam. Systems 23 (2003), no. 3, 869-883
    [DOI: 10.1017/S0143385702001529 | arXiv:math/0206299]
  37. Semi-dispersing billiards with an infinite cusp. II, Chaos 13 (2003), no. 1, 105-111
    [DOI: 10.1063/1.1539802 | arXiv:nlin/0201052]
  38. Semi-dispersing billiards with an infinite cusp. I, Comm. Math. Phys. 230 (2002), no. 1, 133-180
    [DOI: 10.1007/s00220-002-0710-7 | arXiv:nlin/0107041]
  39. Escape orbits and ergodicity in infinite step billiards (with M. Degli Esposti & G. Del Magno), Nonlinearity 13 (2000), no. 4, 1275-1292
    [DOI: 10.1088/0951-7715/13/4/316 | arXiv:chao-dyn/9906017]
  40. Large deviations for ideal quantum systems (with J. L. Lebowitz & H. Spohn), J. Math. Phys. 41 (2000), no. 3, 1224-1243
    [DOI: 10.1063/1.533185 | arXiv:math-ph/9906014]
  41. Classical billiards and quantum large deviations, Ph.D. Thesis, Rutgers University, 1999
    [pdf format]
  42. Caos quantistico cinematico (Kinematic Quantum Chaos), Ph.D. Thesis, Università di Bologna, 1998
    [pdf format (in Italian)]
  43. An infinite step billiard (with M. Degli Esposti & G. Del Magno), Nonlinearity 11 (1998), no. 4, 991-1013
    [DOI: 10.1088/0951-7715/11/4/013 | arXiv:chao-dyn/9709006]
  44. Ergodic properties of the quantum ideal gas in the Maxwell-Boltzmann statistics, J. Math. Phys. 37 (1996), no. 10, 5136-5157
    [DOI: 10.1063/1.531684 | arXiv:chao-dyn/9605005]
  45. Escape orbits for non-compact flat billiards, Chaos 6 (1996), no. 3, 428-431
    [DOI: 10.1063/1.166173 | arXiv:chao-dyn/9602020]
  46. Sulla nozione quantistica di ergodicità (On the quantum notion of ergodicity), Tesi di Laurea (Master's Thesis), Università di Bologna, 1993
    [pdf format (in Italian)]

Other

  1. Metodi a confronto: Didattica Universitaria in USA e in Italia, in: Various Authors (edited by Fabio Rondot), Apprendere, Istruzioni per l'Uso: Atti del Convegno Ottobre 2021, independently published (distributed by Amazon), 2022
    [link to Amazon page (in Italian)]
  2. Scienza e Cultura: impressioni, ParliamoneOra blog, January 2022
    [link to article (in Italian)]
  3. La matematica del distanziamento, in: Aula di Scienze, Zanichelli, 2020
    [link to article (in Italian) | supplementary material (proofs + problems)]
  4. Chi ha paura della matematica?, ParliamoneOra blog, March 2020
    [link to article (in Italian)]

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