List of publications by Lorenzo Bertini

ARTICLES
  1. Boundary driven Brownian gas. PDF
    L. Bertini, G. Posta.
    ALEA, Lat. Am. J. Probab. Math. Stat. 16, 361-388 (2019)

  2. On large deviations of interface motions for statistical mechanics models. PDF
    L. Bertini, P. Buttà, A. Pisante.
    Ann. Henri Poincaré ???? (2019).

  3. Level 2.5 large deviations for continuous-time Markov chains with time periodic rates. PDF
    L. Bertini, R. Chetrite, A. Faggionato, D. Gabrielli.
    Ann. Henri Poincaré 19, 3197-3238 (2018).

  4. Stochastic Allen-Cahn equation with mobility. PDF
    L. Bertini, P. Buttà, A. Pisante.
    NoDEA Nonlinear Differential Equations Appl. 24, 54 (2017).

  5. Stochastic Allen-Cahn approximation of the mean curvature flow: large deviations upper bound. PDF
    L. Bertini, P. Buttà, A. Pisante.
    Arch. Rational Mech. Anal. 224, 659-707 (2017).

  6. Quantitative analysis of the Clausius inequality. PDF
    L. Bertini, A. De Sole, D. Gabrielli, G. Jona Lasinio, C. Landim.
    J. Stat. Mech. Theory Exp. P10018 (2015).

  7. Small noise asymptotic of the Gallavotti-Cohen functional for diffusion processes. PDF
    L. Bertini, G. di Gesú.
    ALEA, Lat. Am. J. Probab. Math. Stat. 12, 743-763 (2015).

  8. Flows, currents, and cycles for Markov Chains: large deviation asymptotics. PDF
    L. Bertini, A. Faggionato, D. Gabrielli.
    Stochastic Processes and their Applications, 125, 2786-2819 (2015).

  9. Donsker-Varadhan asymptotics for degenerate jump Markov processes. PDF
    G. Basile, L. Bertini.
    ALEA, Lat. Am. J. Probab. Math. Stat. 12, 1-23 (2015)

  10. Large deviations of the empirical flow for continuous time Markov chains. PDF
    L. Bertini, A. Faggionato, D. Gabrielli.
    Ann. Inst. H. Poincaré Probab. Statist. 51, 867-900 (2015).

  11. Macroscopic fluctuation theory. PDF
    L. Bertini, A. De Sole, D. Gabrielli, G. Jona Lasinio, C. Landim.
    Rev. Mod. Phys. 87, 593-636 (2015).

  12. From level 2.5 to level 2 large deviations for continuous time Markov chains. PDF
    L. Bertini, A. Faggionato, D. Gabrielli.
    Markov Process. Relat. Fields 20, 545-562 (2014).

  13. Synchronization and random long time dynamics for mean-field plane rotators. PDF
    L. Bertini, G. Giacomin, C. Poquet.
    Probab. Theory Relat. Fields 160, 593-653 (2014).

  14. Drift of phase fluctuations in the ABC model. PDF
    L. Bertini, P. Buttà.
    J. Stat. Phys. 152, 15-36 (2013).

  15. Large deviation principles for nongradient weakly asymmetric stochastic lattice gases. PDF
    L. Bertini, A. Faggionato, D. Gabrielli.
    Ann. Appl. Probab. 23, 1-65 (2013).

  16. Clausius inequality and optimality of quasistatic transformations for nonequilibrium stationary states. PDF
    L. Bertini, D. Gabrielli, G. Jona-Lasinio, C. Landim.
    Phys. Rev. Lett. 110, 020601 (2013).

  17. Convergence of the One-Dimensional Cahn-Hilliard Equation. PDF
    G. Bellettini, L. Bertini, M. Mariani, M. Novaga.
    SIAM J. Math. Anal. 44, 3458-3480 (2012).

  18. Thermodynamic transformations of nonequilibrium states. PDF
    L. Bertini, D. Gabrielli, G. Jona-Lasinio, C. Landim.
    J. Stat. Phys. 149, 773-802 (2012).

  19. Boundary effects in the gradient theory of phase transitions. PDF
    L. Bertini, P. Buttà, A. Garroni.
    SIAM J. Math. Anal. 44, 926-945 (2012).

  20. A variational approach to the stationary solutions of the Burgers equation. PDF
    L. Bertini, M. Ponsiglione.
    SIAM J. Math. Anal. 44, 682-698 (2012).

  21. On the dynamical behavior of the ABC model. PDF
    L. Bertini, N. Cancrini, G. Posta.
    J. Stat. Phys. 144, 1284-1307 (2011).

  22. Action functional and quasi-potential for the Burgers equation in a bounded interval. PDF
    L. Bertini, A. De Sole, D. Gabrielli, G. Jona Lasinio, C. Landim.
    Comm. Pure Appl. Math. 64, 649-696 (2011).

  23. Lagrangian phase transitions in nonequilibrium thermodynamic systems. PDF
    L. Bertini, A. De Sole, D. Gabrielli, G. Jona Lasinio, C. Landim.
    J. Stat. Mech. Theory Exp. L11001 (2010).

  24. Dynamical aspects of mean field plane rotators and the Kuramoto model. PDF
    L. Bertini, G. Giacomin, K. Pakdaman.
    J. Stat. Phys. 138, 270-290 (2010).

  25. Gamma-entropy cost for scalar conservation laws. PDF
    G. Bellettini, L. Bertini, M. Mariani, M. Novaga.
    Arch. Rational Mech. Anal. 195, 261-309 (2010).

  26. Towards a nonequilibrium thermodynamics: A self-contained macroscopic description of driven diffusive systems. PDF
    L. Bertini, A. De Sole, D. Gabrielli, G. Jona Lasinio, C. Landim.
    J. Stat. Phys. 135, 857-872 (2009).

  27. Strong asymmetric limit of the quasi-potential of the boundary driven weakly asymmetric exclusion process. PDF
    L. Bertini, D. Gabrielli, C. Landim.
    Commun. Math. Phys. 289, 311-334 (2009).

  28. Dynamical large deviations for the boundary driven weakly asymmetric exclusion process. PDF
    L. Bertini, M. Mourragui, C. Landim.
    Ann. Probab. 37, 2357-2403 (2009).

  29. Dobrushin states in the φ41 model. PDF
    L. Bertini, S. Brassesco, P. Buttà.
    Arch. Rational Mech. Anal. 190, 477-516 (2008).

  30. Soft and hard wall in a stochastic reaction diffusion equation. PDF
    L. Bertini, S. Brassesco, P. Buttà.
    Arch. Rational Mech. Anal. 190, 307-345 (2008).

  31. Stochastic interacting particle systems out of equilibrium. PDF
    L. Bertini, A. De Sole, D. Gabrielli, G. Jona Lasinio, C. Landim.
    J. Stat. Mech. Theory Exp. P07014 (2007).

  32. Perturbative analysis of disordered Ising models close to criticality. PDF
    L. Bertini, E.N.M. Cirillo, E. Olivieri.
    J. Stat. Phys. 126, 987-1006 (2007).

  33. Large deviations of the empirical current in interacting particle systems. PDF
    L. Bertini, A. De Sole, D. Gabrielli, G. Jona Lasinio, C. Landim.
    Theory Probab. Appl. 51, 2-27 (2007).

  34. Large deviation approach to non equilibrium processes in stochastic lattice gases. PDF
    L. Bertini, A. De Sole, D. Gabrielli, G. Jona Lasinio, C. Landim.
    Bull. Braz. Math. Soc. (N.S.) 37, 611-643 (2006).

  35. Non equilibrium current fluctuations in stochastic lattice gases. PDF
    L. Bertini, A. De Sole, D. Gabrielli, G. Jona Lasinio, C. Landim.
    J. Stat. Phys. 123, 237-276 (2006).

  36. Renormalization group in the uniqueness region: weak Gibbsianity and convergence. PDF
    L. Bertini, E.N.M. Cirillo, E. Olivieri.
    Commun. Math. Phys. 261, 323-378 (2006).

  37. Large deviations for a stochastic model of heat flow. PDF
    L. Bertini, D. Gabrielli, J.L. Lebowitz
    J. Statist. Phys. 121, 843-885 (2005).

  38. Graded cluster expansion for lattice systems. PDF
    L. Bertini, E.N.M. Cirillo, E. Olivieri.
    Commun. Math. Phys. 258, 405-443 (2005).

  39. Current fluctuations in stochastic lattice gases. PDF
    L. Bertini, A. De Sole, D. Gabrielli, G. Jona Lasinio, C. Landim.
    Phys. Rev. Lett. 94, 030601 (2005).

  40. Exclusion processes with degenerate rates: convergence to equilibrium and tagged particle. PDF
    L. Bertini, C. Toninelli.
    J. Statist. Phys. 117, 549-580. (2004)

  41. Minimum dissipation principle in stationary non-equilibrium states. PDF
    L. Bertini, A. De Sole, D. Gabrielli, G. Jona Lasinio, C. Landim.
    J. Statist. Phys. 116, 831-841 (2004).

  42. A combinatorial proof of tree decay of semi-invariants. PDF
    L. Bertini, E.N.M. Cirillo, E. Olivieri.
    J. Statist. Phys. 115, 395-413 (2004).

  43. Interface fluctuations in a conserved system: derivation and long time behavior. PDF
    L. Bertini, P. Buttà, E. Presutti, E. Saada.
    Markov Process. Relat. Fields 9, 1-34 (2003).

  44. Large deviations for the boundary driven symmetric simple exclusion process. PDF
    L. Bertini, A. De Sole, D. Gabrielli, G. Jona Lasinio, C. Landim.
    Math. Phys. Anal. Geom. 6, 231-267 (2003).

  45. Front fluctuations in one dimensional stochastic phase field equations. PDF
    L. Bertini, S. Brassesco, P. Buttà, E. Presutti.
    Ann. Henri Poincaré 3, 29-86 (2002).

  46. Stochastic phase field equations: existence and uniqueness. PDF
    L. Bertini, S. Brassesco, P. Buttà, E. Presutti.
    Ann. Henri Poincaré 3, 87-98 (2002).

  47. The spectral gap for a Glauber-type dynamics in a continuous gas. PDF
    L. Bertini, N. Cancrini, F. Cesi.
    Ann. Inst. H. Poincaré Probab. Statist. 38, 91-108 (2002).

  48. Macroscopic fluctuation theory for stationary non equilibrium states. PDF
    L. Bertini, A. De Sole, D. Gabrielli, G. Jona Lasinio, C. Landim.
    J. Statist. Phys. 107, 635-675 (2002).

  49. Fluctuations in stationary nonequilibrium states of irreversible processes. PDF
    L. Bertini, A. De Sole, D. Gabrielli, G. Jona Lasinio, C. Landim.
    Phys. Rev. Lett. 87, 040601 (2001).

  50. Interface dynamics and Stefan problem from a microscopic conservative model. PDF
    L. Bertini, P. Buttà, B. Rüdiger.
    Rend. Mat. Appl. (7) 19, 547-581 (1999).

  51. Renormalization-group transformation under strong mixing conditions: Gibbsianess and convergence of renormalized interactions. PDF
    L. Bertini, E.N.M. Cirillo, E. Olivieri.
    J. Statist. Phys. 97, 831-915 (1999).

  52. On the long-time behavior of the stochastic heat equation. PDF
    L. Bertini, G. Giacomin.
    Probab. Theory Relat. Fields 114, 279-289 (1999).

  53. Coercive inequalities for Gibbs measures. PDF
    L. Bertini, B. Zegarlinski.
    J. Funct. Anal. 162, 257-286 (1999).

  54. Coercive inequalities for Kawasaki dynamics: the product case. PDF
    L. Bertini, B. Zegarlinski.
    Markov Process. Relat. Fields 5, 125-162 (1999).

  55. The two-dimensional stochastic heat equation: renormalizing a multiplicative noise. PDF
    L. Bertini, N. Cancrini.
    J. Phys. A 31, 615-622 (1998).

  56. Reduction formula for moments of stochastic integrals.
    L. Bertini, N. Cancrini
    J. Math. Phys. 38, 4763-4770 (1997).

  57. Stochastic Burgers and KPZ equations from particle systems. PDF
    L. Bertini, G. Giacomin.
    Commun. Math. Phys. 183, 571-607 (1997).

  58. Derivation of Cahn-Hilliard equations from Ginzburg-Landau models. PDF
    L. Bertini, C. Landim, S. Olla.
    J. Statist. Phys. 88, 365-381 (1997).

  59. The stochastic heat equation: Feynman-Kac formula and intermittency.
    L. Bertini, N. Cancrini
    J. Statist. Phys. 78, 1377-1401 (1995).

  60. The Stochastic Burgers equation. PDF
    L. Bertini, N. Cancrini, G. Jona Lasinio.
    Commun. Math. Phys. 165, 211-232 (1994).

  61. Dynamical fluctuations at the critical point: convergence to a non linear stochastic PDE. PDF
    L. Bertini, E. Presutti, B. Rüdiger, E. Saada.
    Theory Probab. Appl. 38, 586-629 (1993).

  62. Stochastic calculus, stochastic quantization and path integrals: selected topics.
    L. Bertini, G. Jona Lasinio, C. Parrinello.
    Suppl. Progr. Theor. Phys. No. 111, 83-113 (1993).


PROCEEDINGS
  1. Boundary effects on the interface dynamics for the stochastic Allen-Cahn equation.
    L. Bertini, S. Brassesco, P. Buttà.
    In New Trends in Mathematical Physics - Selected contributions of the XVth International Congress on Mathematical Physics, V. Sidoravicius Ed., pp. 87-93. New York, Springer 2009.

  2. Large deviations of the current in stochastic systems. PDF
    L. Bertini
    In Phasenübergänge, Oberwolfach report No. 30/2004, 1592-1594 (2004).

  3. Gibbsian properties and convergence of the iterates for the block averaging transformation. PDF
    L. Bertini, E.N.M. Cirillo, E. Olivieri.
    In Gibbs vs. non-Gibbs in statistical mechanics and related fields (Eindhoven, 2003), Markov Process. Relat. Fields 10,381-394. (2004)

  4. Dynamic fluctuations for Kac and related models.
    L. Bertini.
    In Inhomogeneous random systems (Cergy-Pontoise, 2001), Markov Process. Relat. Fields 8, 365-379 (2002).

  5. A microscopic model of phase field type.
    L. Bertini, P. Buttà, B. Rüdiger.
    In Seminar on Stochastic Analysis, Random Fields and Applications (Ascona, 1996), 63-71, Progr. Probab. 45, Birkhäuser, Basel, 1999.

  6. Stochastically forced Burgers equation.
    L. Bertini, N. Cancrini, G. Jona Lasinio.
    In On Three Levels. Micro-, Meso-, and Macro-Approaches in Physics, M. Fannes, C. Maes, A. Verbeure eds. NATO ASI Series Vol. B 324, 265-269. New York, Plenum Press 1994.

  7. Burgers equation forced by conservative or nonconservative noise.
    L. Bertini, N. Cancrini, G. Jona Lasinio.
    In Stochastic Analysis and Applications in Physics, A.I. Cardoso et. al. eds. NATO ASI Series Vol. C 449, 35-44. Dordrecht, Kluwer Academic Publishers 1994.




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