Publications of Luc Rey-Bellet

  1. Hyemin Gu, Markos A. Katsoulakis, Luc Rey-Bellet, and Benjamin J. Zhang.
    Combining Wasserstein-1 and Wasserstein-2 proximals: robust manifold learning via well-posed generative flows.
    Submitted.
    arXiv:2407.11901

  2. Jeremiah Birrell, Markos A. Katsoulakis, Luc Rey-Bellet, Benjamin Zhang, and Wei Zhu.
    Nonlinear denoising score matching for enhanced learning of structured distributions.
    Submitted.
    arXiv:2405.15625

  3. Ziyu Chen, Hyemin Gu, Markos A. Katsoulakis, Luc Rey-Bellet, and Wei Zhu.
    Learning heavy-tailed distributions with Wasserstein-proximal-regularized α-divergences. Submitted.
    arXiv:2405.13962

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

  5. 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)

  6. 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.
    To appear in Siam Journal on Mathematics of Data Science (2024).
    arXiv:2210.17230

  7. Jeremiah Birrell, Paul Dupuis, Markos Katsoulakis, Yannis Pantazis, and 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

  8. Jeremiah Birrell, Markos Katsoulakis, Luc Rey-Bellet, and 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)

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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

  30. 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

  31. 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 .

  32. 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

  33. 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

  34. 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

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

  36. 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

  37. 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

  38. 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

  39. 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

  40. 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

  41. 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

  42. 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

  43. 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

  44. 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

  45. 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

  46. 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

  47. 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

  48. 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

  49. 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

  50. 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

  51. 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

  52. 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

  53. 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

  54. 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

  55. 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

  56. 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

  57. 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

  58. 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

  59. 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

  60. 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