Luc Rey-Bellet

Professor, Department of Mathematics and Statistics, UMass Amherst

Contact information

Mailing Address:
Department of Mathematics & Statistics
Lederle Graduate Research Tower, Box 34515
University of Massachusetts
Amherst, MA 01003-4515
USA

Office: LGRT 1423 K
Office Phone: 413 545 6020
Fax: 413-545-1801
Email: luc@math.umass.edu

Teaching

Fall 2022: Math 605, Probability Theory 1

Syllabus, Class homepage on Moodle

Fall 2022: Math 797TT, Information Theory and Optimal Transport

Syllabus, Class homepage on Moodle

Some earlier classes:

S20:Stat515, Stat I -- S20:Math697U, Stochastic Processes -- F19:Stat605, Probability -- S19:Math456, Math Modeling -- S18:Math697U, Stochastic processes -- F17:Math 331, ODEs -- F17:Stat605, Probability -- S17:Math331, ODEs -- S17:Math523, Analysis I -- S16:M456, Math Modeling -- S16:Math523, Analysis I -- F15:Math797AB, Agent-Based Modeling -- S15:Math456, Math Modeling -- S15:Math797MR, Information Theory -- F14:Math697U, Stochastic Processes -- S14:Math331, ODEs -- S14:Math624, Real Analysis II -- F13:Math623 Real Analysis I -- S13:Math707fn Functional Analysis-- S13:Math456, Math Modeling -- S12:Math624 Real Analysis I -- S12:Math456, Math Modeling -- F11:Math623, Real Analysis I -- F10:Math623, Real Analysis I -- F10:Math123H, Calc I -- F10:Math123H, Calc I-- S10:Math697, Stochastic Processes -- S10:Math331, ODEs -- F09:Math697eg, Evolutionary Game Theory -- F08:Math331,ODEs -- F08:Math645, ODEs and Dynamical Systems -- S08:Math331, ODEs -- F07:Math331, ODEs -- F07:Math697, Stochastic Processes -- S07:Math624, Real Analysis II-- F06:Math623, Real Analysis I-- F06:Math131, Calc I-- S06:M597/697, Stochastic Processes -- F05:Stat515, Stat I -- F05:Math645, ODE and Dynamical Systems -- S05:Math131, Calc I -- S05:Math646, Ergodic Theory -- F04:Math645, ODEs and Dynamical Systems -- S04:Math132, Calc II -- F03:Math697, Stochastic Processes -- S03:Math421, Complex Variables -- S03:Math132, Calc II -- F02:Math131, Calc I

Research

My research interests are in Statistical Mechanics, Applied Probability, Game Theory, Uncertainty Quantification and Machine Learning.

A detailed CV

Google Scholar page Research Gate Page Papers on ArXiv MathSciNet Page Orcid Page

Publication List

  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. To be published in the Procceedings of The Eleventh International Conference on Learning Representations (ICLR 2023).
    arXiv:2210.04974