Publications of Luc Rey-Bellet
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Low-temperature phase diagrams of quantum lattice systems. II. Convergent perturbation
expansions and stability in systems with infinite degeneracy
(with Nilanjana Datta, Jürg Fröhlich, and Roberto Fernandez).
Helvetica Physica Acta 69, 752--820 (1996).
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Low-temperature phase diagrams of quantum lattice systems. III. Examples
(with Jürg Fröhlich).
Helvetica Physica Acta 69, 821--849 (1996).
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Non-equilibrium statistical mechanics of anharmonic chains coupled to two heat
baths at different temperatures
(with Jean-Pierre Eckmann and Claude-Alain Pillet).
Communications in Mathematical Physics 201, 657--697 (1999).
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Entropy production in non-linear, thermally driven Hamiltonian systems
(with Jean-Pierre Eckmann and Claude-Alain Pillet).
Journal of Statistical Physics 95, 305--331 (1999).
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Asymptotic behavior of thermal non-equilibrium steady states for a driven chain of anharmonic oscillators
(with Lawrence E. Thomas).
Communications in Mathematical Physics 215, 1--24 (2000).
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Fourier Law: A challenge to theorists
(with Federico Bonetto and Joel Lebowitz).
In: Mathematical Physics 2000, A. Fokas, A. Grigoryan, T. Kibble, and B. Zegarlinski (Eds.) Imperial College Press, London 2000.
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Quantum lattice systems at intermediate temperature
(with Jürg Fröhlich and Daniel Ueltschi).
Communications in Mathematical Physics 224, 33--63 (2001).
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Exponential convergence to non-equilibrium stationary states in classical statistical mechanics
(with Lawrence E. Thomas).
Communications in Mathematical Physics 225, 305--329 (2002).
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Fluctuations of the entropy production in anharmonic chains
(with Lawrence E. Thomas).
Annales Henri Poincaré 3 483--502 (2002).
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Statistical mechanics of anharmonic lattices.
In: Advances in Differential Equations and Mathematical Physics,
AMS Contemporary Mathematics Series 327, 283--298 (2003).
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Low regularity solutions to a gently stochastic nonlinear wave equation in nonequilibrium statistical mechanics
(with Lawrence E. Thomas).
Stochastic Processes and their Applications. 115, 1041--1059 (2005).
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Large deviations in quantum lattice systems: one phase region
(with Marco Lenci).
Journal of Statistical Physics 119, 715--746 (2005).
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Nonequilibrium statistical mechanics of open classical systems.
In: XIVth International Conference on Mathematical Physics, Lisbon, Portugal, 28 July -- 2 August 2003, World Scientific 2006.
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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.
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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.
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Fourier Law (with Federico Bonetto).
In: Encyclopedia of Mathematical Physics. J.-P. Francoise, G. L. Naber, Tsou S.T. (Eds.) Elsevier 2006.
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Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems
(with Markos Katsoulakis, Petr Plecháč and Dimitrios Tsagkarogiannis).
ESAIM: Mathematical Modelling and Numerical Analysis
41, 627--660 (2007).
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Mathematical strategies and error quantification in the coarse-graining of extensive systems
(with Markos Katsoulakis, Petr Plecháč and Dimitrios Tsagkarogiannis).
Journal of Non Newtonian Fluid Mechanics 152, 101--112 (2008).
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Large deviations in nonuniformly hyperbolic dynamical systems
(with Lai-Sang Young). Ergodic Theory and Dynamical Systems 28, 587-612 (2008).
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Numerical and statistical methods for the coarse-graining
of many-particle stochastic systems (with Markos Katsoulakis and Petr Plecháč).
Journal of Scientific Computing 37 , 43--71 (2008).
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Multi-body interactions in coarse-graining schemes of extended systems
(with Sasanka Are, Markos Katsoulakis , and Petr Plecháč).
SIAM Journal on Scientific Computing 31 987-1015 (2008).
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A note on the non-commutative Laplace-Varadhan integral lemma
(With Wojciech De Roeck, Christian Maes and Karel Netočný).
Reviews in Mathematical Physics 22 , 839--858 (2010).
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Entropic fluctuations in statistical mechanics I. Classical dynamical systems
(with Claude-Alain Pillet and Vojkan Jaksic).
Nonlinearity 24 , 699-763 (2011).
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Ruelle-Lanford functions and large deviations for asymptotically decoupled quantum spin systems. (with Yoshiko Ogata).
Reviews in Mathematical Physics 23 , 211--232 (2011).
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Absolute continuity of Brownian bridges under certain gauge transformations
(with Andrea Nahmod, Scott Sheffield, and Gigliola Staffilani).
Mathematical Research Letters 18 , 875--887 (2011).
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Decompositions of two player games: potential, zero-sum, and stable games
(with Sung-Ha Hwang). Unpublished.
arXiv:1106.3552 PDF file .
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Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS
(with Andrea Nahmod, Hiro Oh, and Gigliola Staffilani).
Journal of the European Mathematical Society 14 , 1275--1330 (2012).
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Deterministic equations for stochastic spatial evolutionary games
(with Sung-Ha Hwang and Markos Katsoulakis).
Theoretical Economics 8 , 829-874 (2013).
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Coarse-graining schemes for stochastic lattice systems with short and long-range interactions
(with M. Katsoulakis, P. Plecháč and D. Tsagkarogiannis).
Mathematics of Computation 83, 288, 1757--1793 (2014).
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- Measuring the irreversibility of numerical schemes for reversible stochastic differential equations
(with Markos Katsoulakis and Yannis Pantazis).
ESAIM: Mathematical Modelling and Numerical Analysis 48 , 1351--1379 (2014).
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- Irreversible Langevin samplers and variance reduction: a large deviation approach
(with Konstantinos Spiliopoulos).
Nonlinearity 28 , 2081-2103, (2015).
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- Variance reduction for irreversible Langevin samplers and diffusion on graphs
(with Konstantinos Spiliopoulos).
Electronic Communications in Probability 20, Article 15, 1--16 (2015).
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Strategic decompositions of normal form games: potential games and zero-sum games
(with Sung-Ha Hwang). Submitted. arXiv:1602.06648
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Simple characterizations of potential games and zero-sum games (with Sung-Ha Hwang).
Submitted. arXiv:1602.04410
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- Information metrics for long-time errors in splitting schemes for stochastic dynamics and parallel kinetic Monte Carlo
(with Konstantinos Gourgoulias and Markos Katsoulakis).
SIAM Journal on Scientific Computing 38 , No. 6, A3808--A3832 (2016).
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Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics (with Georgios Arampatzis and Markos Katsoulakis).
Journal of Chemical Physics 144, 104107 (2016).
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- Improving the convergence of reversible samplers (with Konstantinos Spiliopoulos).
Journal of Statistical Physics 164, 472--494 (2016).
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- Uncertainty quantification for generalized Langevin dynamics (with Eric Hall and Markos Katsoulakis).
Journal of Chemical Physics 145, 224108 (2016).
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- Information criteria for quantifying loss of reversibility in parallelized KMC (with Konstantinos Gourgoulias and Markos Katsoulakis).
Journal of Computational Physics 328, 438--454 (2017).
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- Scalable information inequalities for uncertainty quantification
(with Markos Katsoulakis and Jie Wang).
Journal of Computational Physics 336, 513--545 (2017)
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Positive feedback in coordination games: stochastic evolutionary dynamics and the logit choice rule (with Sung-Ha Hwang). Submitted. arXiv:1701.04870 PDF file
- How biased is your model? Concentration inequalities, information and model bias (with Konstantinos Gourgoulias, Markos Katsoulakis, and Jie Wang): To be published in IEEE Transactions on Information Theory. arXiv:1706.10260 PDF file
- Fluctuations of the entropy production for the Lorentz gas under small external forces (with Mark Demers and Hongkun Zhang).
Communications in Mathematical Physics 363 , 699-740 (2018)
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- Non-equilibrium steady states for networks of oscillators (with Noé Cuneo, Jean-Pierre Eckmann and Martin Hairer).
Electronic Journal of Probability 23 paper no. 55, 28 pp. (2018)
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- Sensitivity analysis for rare rvents based on Rényi divergence (with Paul Dupuis, Markos Katoulakis and Yannis Pantazis). To be published in Annals of Applied Probability. arXiv:1805.06917 PDF file
- Uncertainty quantification for Markov processes via variational principles and functional inequalities (with Jeremiah Birrell). Submitted. arXiv:1812.05174 PDF file
- Robustness of dynamical quantities of interest via goal-oriented information theory (with Jeremiah Birrell and Markos Katsoulakis).
Submitted. arXiv:1906.09282 PDF file
- Concentration inequalities and performance guarantees for hypocoercive MCMC samplers (with Jeremiah Birrell). Submitted. arXiv:1907.11973 PDF file