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

  1. Continuous-time random walk between Lévy-spaced targets in the real line (with A. Bianchi & F. Pène), preprint
    [
    arXiv:1806.02278]
  2. Pointwise convergence of Birkhoff averages for global observables (with S. Munday), preprint
    [arXiv:1804.05359]
  3. Infinite mixing for one-dimensional maps with an indifferent fixed point (with C. Bonanno & P. Giulietti), preprint
    [arXiv:1708.09369]
  4. 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]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. 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]
  12. 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]
  13. Exactness, K-property and infinite mixing, Publ. Mat. Urug. 14 (2013), 159-170
    [link to issue | arXiv:1212.4099]
  14. 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]
  15. 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]
  16. 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]
  17. 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]
  18. 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]
  19. On infinite-volume mixing, Comm. Math. Phys. 298 (2010), no. 2, 485-514
    [DOI: 10.1007/s00220-010-1043-6 | arXiv:0906.4059]
  20. 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]
  21. 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]
  22. Recurrence for persistent random walks in two dimensions, Stoch. Dyn. 7 (2007), no. 1, 53-74
    [DOI: 10.1142/S0219493707001937 | arXiv:math/0507411]
  23. Typicality of recurrence for Lorentz gases, Ergodic Theory Dynam. Systems 26 (2006), no. 3, 799-820
    [DOI: 10.1017/S0143385706000022 | arXiv:math/0410355]
  24. 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]
  25. 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]
  26. Aperiodic Lorentz gas: recurrence and ergodicity, Ergodic Theory Dynam. Systems 23 (2003), no. 3, 869-883
    [DOI: 10.1017/S0143385702001529 | arXiv:math/0206299]
  27. Semi-dispersing billiards with an infinite cusp. II, Chaos 13 (2003), no. 1, 105-111
    [DOI: 10.1063/1.1539802 | arXiv:nlin/0201052]
  28. 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]
  29. 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]
  30. 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]
  31. Classical billiards and quantum large deviations, Ph.D. Thesis, Rutgers University, 1999
    [pdf format]
  32. Caos quantistico cinematico (Kinematic Quantum Chaos), Ph.D. Thesis, Università di Bologna, 1998
    [(in Italian) pdf format]
  33. 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]
  34. 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]
  35. Escape orbits for non-compact flat billiards, Chaos 6 (1996), no. 3, 428-431
    [DOI: 10.1063/1.166173 | arXiv:chao-dyn/9602020]

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