Publications of Luc Rey-Bellet

  1. Nilanjana Datta, Roberto Fernandez, Jürg Fröhlich, and Luc Rey-Bellet, Low-temperature phase diagrams of quantum lattice systems. II. Convergent perturbation expansions and stability in systems with infinite degeneracy, Helvetica Physica Acta 69 (1996), 5-6, pp. 752–820.
    DOI: 10.5169/seals-116979   MR1428028   Reprint in PDF  

  2. Jürg Fröhlich and Luc Rey-Bellet, Low-temperature phase diagrams of quantum lattice systems. III. Examples, Helvetica Physica Acta 69 (1996), 5-6, pp. 821–849.
    DOI: 10.5169/seals-116980   MR1428029   Reprint in PDF

  3. Jean-Pierre Eckmann, Claude-Alain Pillet, and Luc Rey-Bellet, Non-equilibrium statistical mechanics of anharmonic chains coupled to two heat baths at different temperatures, Communications in Mathematical Physics 201 (1999), no. 3, pp. 657–697.
    DOI: 10.1007/s002200050572   MR1685893   Reprint in PDF

  4. Jean-Pierre Eckmann, Claude-Alain Pillet, and Luc Rey-Bellet, Entropy production in non-linear, thermally driven Hamiltonian systems, Journal of Statistical Physics 95 (1999), no. 1-2, pp. 305–331.
    DOI:10.1023/A:1004537730090   MR1705589   Reprint in PDF

  5. Lawrence E. Thomas and Luc Rey-Bellet, Asymptotic behavior of thermal non-equilibrium steady states for a driven chain of anharmonic oscillators, Communications in Mathematical Physics 215 (2000), no.1, pp. 1–24.
    DOI: 10.1007/s002200000285   MR1799873   Reprint in PDF

  6. Federico Bonetto, Joel Lebowitz, and Luc Rey-Bellet, Fourier Law: A challenge to theorists, In: Mathematical Physics 2000, A. Fokas, A. Grigoryan, T. Kibble, and B. Zegarlinski (Eds.) Imperial College Press, London 2000, pp. 128–150.
    DOI:10.1142/9781848160224_0008   MR1773043   Reprint in PDF

  7. Jürg Fröhlich, Luc Rey-Bellet, and Daniel Ueltschi, Quantum lattice systems at intermediate temperature, Communications in Mathematical Physics 224 (2001), no. 1, pp. 33–63.
    DOI: 10.1007/s002200100530   MR1869003   Reprint in PDF

  8. Lawrence E. Thomas and Luc Rey-Bellet, Exponential convergence to non-equilibrium stationary states in classical statistical mechanics, Communications in Mathematical Physics 225 (2002), no.1, pp. 305–329.
    DOI: 10.1007/s002200100583   MR1889227   Reprint in PDF

  9. Lawrence E. Thomas and Luc Rey-Bellet, Fluctuations of the entropy production in anharmonic chains, Annales Henri Poincaré 3 (2002), no.3, pp. 483–502.
    DOI: 10.1007/s00023-002-8625-6   MR1915300   Reprint in PDF

  10. Luc Rey-Bellet Statistical mechanics of anharmonic lattices, In: Advances in Differential Equations and Mathematical Physics, AMS Contemporary Mathematics Series 327 (2003), pp. 283–298.
    DOI:   MR1991548   Reprint in PDF

  11. Lawrence E. Thomas and Luc Rey-Bellet, Low regularity solutions to a gently stochastic nonlinear wave equation in nonequilibrium statistical mechanics, Stochastic Processes and their Applications 115 (2005), no.6, pp. 1041–1059. (2005).
    DOI: 10.1016/j.spa.2005.02.003   MR2138813   Reprint in PDF

  12. Marco Lenci and Luc Rey-Bellet, Large deviations in quantum lattice systems: one phase region, Journal of Statistical Physics 119 (2005), no. 3-4, pp. 715–746.
    DOI: 10.1007/s10955-005-3015-3   MR2151220   Reprint in PDF

  13. Luc Rey-Bellet, Nonequilibrium statistical mechanics of open classical systems, In: XIVth International Conference on Mathematical Physics, Lisbon, Portugal, 28 July – 2 August 2003, World Scientific 2006, pp. 447–454
    DOI: 10.1142/9789812704016_0043   MR2227858   PDF file

  14. Luc Rey-Bellet Ergodic Properties of Markov Processes, In: Quantum Open Systems II. The Markovian approach. Stéphane Attal, Alain Joye, Claude-Alain Pillet (Eds.), Lecture Notes in Mathematics 1881, Berlin: Springer, 2006, pp. 1–39.
    DOI:10.1007/3-540-33966-3_1   MR2248986   Reprint in PDF

  15. Luc Rey-Bellet, Open Classical Systems, In: Quantum Open Systems II. The Markovian approach. Stéphane Attal, Alain Joye, Claude-Alain Pillet (Eds.), Lecture Notes in Mathematics 1881, Berlin: Springer, 2006, pp. 41–78.
    DOI: 10.1007/3-540-33966-3_2   MR2248987   Reprint in PDF

  16. Federico Bonetto and Luc Rey-Bellet, Fourier Law, In: Encyclopedia of Mathematical Physics. J.-P. Francoise, G. L. Naber, S.T. Tsou (Eds.), Elsevier 2006, pp. 374–379.
    Reprint in PDF

  17. Markos Katsoulakis, Petr Plecháč, Luc Rey-Bellet, and Dimitrios Tsagkarogiannis, Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems, ESAIM: Mathematical Modelling and Numerical Analysis 41 (2007), no.3, pp. 627–660.
    DOI: 10.1051/m2an:2007032   MR2355714   Reprint in PDF

  18. Markos Katsoulakis, Petr Plecháč, Luc Rey-Bellet, and Dimitrios Tsagkarogiannis, Mathematical strategies in the coarse-graining of extensive systems: error quantification and adaptivity, Journal of Non Newtonian Fluid Mechanics 152 (2008), pp. 101–112.
    DOI: 10.1016/j.jnnfm.2007.05.005     Reprint in PDF

  19. Lai-Sang Young and Luc Rey-Bellet, Large deviations in nonuniformly hyperbolic dynamical systems, Ergodic Theory and Dynamical Systems 28 (2008), no.2, pp. 587-612.
    DOI:10.1017/S0143385707000478   MR2408394   Reprint in PDF

  20. Markos Katsoulakis, Petr Plecháč, and Luc Rey-Bellet, Numerical and statistical methods for the coarse-graining of many-particle stochastic systems, Journal of Scientific Computing 37 (2008), no.1, pp. 43–71.
    DOI: 10.1007/s10915-008-9216-6   MR2442973   Reprint in PDF

  21. Sasanka Are, Markos Katsoulakis, Petr Plecháč, and Luc Rey-Bellet, Multi-body interactions in coarse-graining schemes of extended systems, SIAM Journal on Scientific Computing 31 (2008/2009), no.2, pp. 987–1015.
    DOI: 10.1137/080713276   MR2466145   Reprint in PDF

  22. Wojciech De Roeck, Christian Maes, Karel Netočný, and Luc Rey-Bellet, A note on the non-commutative Laplace-Varadhan integral lemma, Reviews in Mathematical Physics 22 (2010), no.7, pp. 839–858.
    DOI: 10.1142/S0129055X10004089   MR2673696   Reprint in PDF

  23. Vojkan Jaksic, Claude-Alain Pillet, and Luc Rey-Bellet, Entropic fluctuations in statistical mechanics I. Classical dynamical systems, Nonlinearity 24 (2011), no.3, pp. 699–763.
    DOI: 10.1088/0951-7715/24/3/003   MR2765481   Reprint in PDF

  24. Yoshiko Ogata and Luc Rey-Bellet, Ruelle-Lanford functions and large deviations for asymptotically decoupled quantum spin systems, Reviews in Mathematical Physics 23 (2011), no.2, pp. 211–232.
    DOI: 10.1142/S0129055X11004291   MR2786227   Reprint in PDF

  25. Andrea Nahmod, Luc Rey-Bellet, Scott Sheffield, and Gigliola Staffilani, Absolute continuity of Brownian bridges under certain gauge transformations, Mathematical Research Letters 18 (2011), no.5, pp. 875–887.
    DOI: 10.4310/MRL.2011.v18.n5.a6   MR2875861   Reprint in PDF

  26. Sung-Ha Hwang and Luc Rey-Bellet, Decompositions of two player games: potential, zero-sum, and stable games, Unpublished (2011).
    arXiv:1106.3552 .

  27. Andrea Nahmod, Hiro Oh, Luc Rey-Bellet, and Gigliola Staffilani, Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS, Journal of the European Mathematical Society 14 (2012), no.4, pp. 1275–1330.
    DOI: 10.4171/JEMS/333   MR2928851   Reprint in PDF

  28. Sung-Ha Hwang, Luc Rey-Bellet, and Markos Katsoulakis, Deterministic equations for stochastic spatial evolutionary games, Theoretical Economics 8 (2013), no.3, pp. 829–874.
    DOI: 10.3982/TE829   MR3106962   Reprint in PDF

  29. M. Katsoulakis, P. Plecháč, Luc Rey-Bellet, and D. Tsagkarogiannis, Coarse-graining schemes for stochastic lattice systems with short and long-range interactions, Mathematics of Computation 83 (2014), no.288, pp. 1757–1793.
    DOI: 10.1090/S0025-5718-2014-02806-8   MR3194129   Reprint in PDF

  30. Markos Katsoulakis, Yannis Pantazis, and Luc Rey-Bellet, Measuring the irreversibility of numerical schemes for reversible stochastic differential equations, ESAIM: Mathematical Modelling and Numerical Analysis 48 (2014), no.5, pp. 1351–1379.
    DOI: 10.1051/m2an/2013142   MR3264357   Reprint in PDF .

  31. Konstantinos Spiliopoulos and Luc Rey-Bellet, Irreversible Langevin samplers and variance reduction: a large deviation approach, Nonlinearity 28 (2015), no.7, pp. 2081–2103.
    DOI: 10.1088/0951-7715/28/7/2081   MR3366637   Reprint in PDF

  32. Konstantinos Spiliopoulos and Luc Rey-Bellet, Variance reduction for irreversible Langevin samplers and diffusion on graphs, Electronic Communications in Probability 20 (2015), no. 15, 16pp.
    DOI: 10.1214/ECP.v20-3855   MR3314650   Reprint in PDF

  33. Konstantinos Gourgoulias, Markos Katsoulakis, and Luc Rey-Bellet, Information metrics for long-time errors in splitting schemes for stochastic dynamics and parallel kinetic Monte Carlo, SIAM Journal on Scientific Computing 38 (2016), no. 6, pp. A3808–A3832.
    DOI: 10.1137/15M1047271   MR3582415   Reprint in PDF

  34. Georgios Arampatzis, Markos Katsoulakis, and Luc Rey-Bellet, Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics, Journal of Chemical Physics 144 (2016), 104107.
    DOI: 10.1063/1.4943388   Reprint in PDF

  35. Konstantinos Spiliopoulos and Luc Rey-Bellet, Improving the convergence of reversible samplers, Journal of Statistical Physics 164 (2016), no.3, 472–494.
    DOI: 10.1007/s10955-016-1565-1   MR3519206   Reprint in PDF

  36. Eric Hall, Markos Katsoulakis, and Luc Rey-Bellet, Uncertainty quantification for generalized Langevin dynamics, Journal of Chemical Physics 145 (2016), 224108.
    DOI: 10.1063/1.4971433   Reprint in PDF

  37. Konstantinos Gourgoulias, Markos Katsoulakis, and Luc Rey-Bellet, Information criteria for quantifying loss of reversibility in parallelized KMC, Journal of Computational Physics 328 (2017), pp. 438–454. DOI: 10.1016/j.jcp.2016.10.031   MR3571894   Reprint in PDF

  38. Markos Katsoulakis, Luc Rey-Bellet, and Jie Wang, Scalable information inequalities for uncertainty quantification, Journal of Computational Physics 336 (2017), pp. 513–545.
    DOI: 10.1016/j.jcp.2017.02.020   Reprint in PDF

  39. Noé Cuneo, Jean-Pierre Eckmann, Martin Hairer, and Luc Rey-Bellet, Non-equilibrium steady states for networks of oscillators, Electronic Journal of Probability 23 (2018), paper no. 55, 28 pp.
    DOI: 10.1214/18-EJP177   MR3814249   Reprint in PDF

  40. Mark Demers, Luc Rey-Bellet,and Hongkun Zhang, Fluctuations of the entropy production for the Lorentz gas under small external forces, Communications in Mathematical Physics 363 (2018), no. 2, pp. 699–740.
    DOI: 10.1007/s00220-018-3228-3   MR3851827   Reprint in PDF

  41. Sung-Ha Hwang and Luc Rey-Bellet, Strategic decompositions of normal form games: potential games and zero-sum games, Games and Economic Behavior 122, (2020), pp. 370–390.
    DOI: 10.1016/j.geb.2020.05.003   Reprint in PDF file   Supplementary Materials

  42. Sung-Ha Hwang and Luc Rey-Bellet, Simple characterizations of potential games and zero-sum equivalent games, Journal of Economic Theory and Econometrics, 31 (2020), pp. 1–13.
    Online version   Reprint in PDF .

  43. Konstantinos Gourgoulias, Markos Katsoulakis, Luc Rey-Bellet, and Jie Wang, How biased is your model? Concentration inequalities, information and model bias, IEEE Transactions on Information Theory 66 (2020), no.5, pp. 3079–3097.
    DOI: 10.1109/TIT.2020.2977067   Reprint in PDF

  44. Jeremiah Birrell and Luc Rey-Bellet, Uncertainty quantification for Markov processes via variational principles and functional inequalities, SIAM/ASA Journal on Uncertainty Quantification, 8 (2020), no. 2, pp. 539–572.
    DOI: 10.1137/19M1237429   Reprint in PDF

  45. Paul Dupuis, Markos Katoulakis, Yannis Pantazis, and Luc Rey-Bellet, Sensitivity analysis for rare events based on Rényi divergence, The Annals of Applied Probability, 30 (2020), no.4, pp. 1507-1533.
    DOI:10.1214/19-AAP1468   Reprint in PDF

  46. Jeremiah Birrell and Luc Rey-Bellet Concentration inequalities and performance guarantees for hypocoercive MCMC samplers, Submitted. arXiv:1907.11973   Preprint in PDF

  47. Jeremiah Birrell, Markos Katsoulakis, and Luc Rey-Bellet, Quantification of model uncertainty on path-space via goal-oriented relative entropy, ESAIM: Mathematical Modeling and Numerical Analysis 55 (2021), no.1, pp. 131-169.
    DOI: 10.1051/m2an/2020070   Reprint in PDF

  48. Sung-Ha Hwang and Luc Rey-Bellet, Positive feedback in coordination games: stochastic evolutionary dynamics and the logit choice rule, Games and Economic Behavior 126 (2021), pp. 355-373
    DOI: 10.1016/j.geb.2021.01.003   Reprint in PDF   Supplementary Materials

  49. Jeremiah Birrell, Paul Dupuis, Markos A. Katsoulakis, Luc Rey-Bellet, and Jie Wang, Distributional robustness and uncertainty quantification for rare events, Preprint. arXiv:1911.09580   Preprint in PDF

  50. Jeremiah Birrell, Paul Dupuis, Markos A. Katsoulakis, Luc Rey-Bellet, and Jie Wang, A variational formula for Rényi divergences, SIAM Journal on Mathematics of Data Science 3 (2021), no. 4, pp. 1093-1116
    DOI: 10.1137/20M1368926   Reprint in PDF

  51. Jeremiah Birrell, Paul Dupuis, Markos Katsoulakis, Yannis Pantazis, and Luc Rey-Bellet, (f,Γ)-Divergences: Interpolating between f-Divergences and Integral Probability Metrics, Journal of Machine Learning Research 23 (2022), paper 39, pp.1−70.
    Online Version   Reprint in PDF

  52. Panagiota Birmpa, Jinchao Feng, Markos Katsoulakis and Luc Rey-Bellet, Model Uncertainty and Correctability for Directed Graphical Models, SIAM/ASA Journal on Uncertainty Quantification 10 (2022), no.4, pp 1461–1512.
    DOI:10.1137/21M1434453   Reprint in PDF

  53. Jeremiah Birrell, Markos Katsoulakis, Luc Rey-Bellet, Wei Zu Structure-preserving GANs, Proceedings of the 39th International Conference on Machine Learning, PMLR 162 (2022) pp.1982-2020.
    Online Version   Reprint in PDF (including supplementary materials)

  54. Jeremiah Birrell, Paul Dupuis, Markos Katsoulakis, Yannis Pantazis, Luc Rey-Bellet Function-space regularized Rényi divergences,
    Procceedings of The Eleventh International Conference on Learning Representations (ICLR 2023).
    Poster and Slides   Open review   Reprint in PDF

  55. Hyemin Gu, Panagiota Birmpa, Yannis Pantazis, Luc Rey-Bellet, and Markos A. Katsoulakis, Lipschitz-regularized gradient flows and generative particle algorithms for high-dimensional scarce data, Submitted.
    arXiv:2210.17230

  56. Ziyu Chen, Markos A. Katsoulakis, Luc Rey-Bellet, and Wei Zhu, Sample Complexity of Probability Divergences under Group Symmetry, Proceedings of 40th International Conference on Machine Learning, PMLR 202 (2023) pp. 4713-4734
    Online Version   Reprint in PDF (including supplementary materials)

  57. Ziyu Chen, Markos A. Katsoulakis, Luc Rey-Bellet, and Wei Zhu, Statistical Guarantees of Group-Invariant GANs, Submitted.
    arXiv:2305.13517