Marco Lenci: Research Page

1. 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]
2. 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]
3. 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]
4. 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]
5. 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]
6. 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]
7. 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]
8. 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]
9. 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]
10. 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]
11. 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]
12. 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]
13. 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]
14. 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]
15. 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]
16. 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]
17. 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]
18. 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]
19. 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]
20. 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]
21. Exactness, K-property and infinite mixing, Publ. Mat. Urug. 14 (2013), 159-170
    [link to issue | arXiv:1212.4099]
22. 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]
23. 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]
24. 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]
25. 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]
26. 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]
27. On infinite-volume mixing, Comm. Math. Phys. 298 (2010), no. 2, 485-514
    [DOI: 10.1007/s00220-010-1043-6 | arXiv:0906.4059]
28. 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]
29. 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]
30. Recurrence for persistent random walks in two dimensions, Stoch. Dyn. 7 (2007), no. 1, 53-74
    [DOI: 10.1142/S0219493707001937 | arXiv:math/0507411]
31. Typicality of recurrence for Lorentz gases, Ergodic Theory Dynam. Systems 26 (2006), no. 3, 799-820
    [DOI: 10.1017/S0143385706000022 | arXiv:math/0410355]
32. 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]
33. 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]
34. Aperiodic Lorentz gas: recurrence and ergodicity, Ergodic Theory Dynam. Systems 23 (2003), no. 3, 869-883
    [DOI: 10.1017/S0143385702001529 | arXiv:math/0206299]
35. Semi-dispersing billiards with an infinite cusp. II, Chaos 13 (2003), no. 1, 105-111
    [DOI: 10.1063/1.1539802 | arXiv:nlin/0201052]
36. 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]
37. 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]
38. 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]
39. Classical billiards and quantum large deviations, Ph.D. Thesis, Rutgers University, 1999
    [pdf format]
40. Caos quantistico cinematico (Kinematic Quantum Chaos), Ph.D. Thesis, Università di Bologna, 1998
    [pdf format (in Italian)]
41. 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]
42. 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]
43. Escape orbits for non-compact flat billiards, Chaos 6 (1996), no. 3, 428-431
    [DOI: 10.1063/1.166173 | arXiv:chao-dyn/9602020]
44. 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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