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Non-Equilibrium Statistical Mechanics

Systèmes Mécaniques Couplés à des Bains Thermiques de Températures Différentes
Diploma Thesis, Univ. of Geneva (1998) Under the direction of J.-P. Eckmann
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Non-Equilibrium Statistical Mechanics of Strongly Anharmonic Chains of Oscillators
Written in collaboration with J.-P. Eckmann.
Commun. Math. Phys. 212 (2000), no 1, pp. 105-164 Published version
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Spectral Properties of Hypoelliptic Operators
Written in collaboration with J.-P. Eckmann.
Commun. Math. Phys. 235 (2003), no 2, pp. 233-253 Published version
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Slow Energy Dissipation in Chains of Anharmonic Oscillators
Written in collaboration with J. Mattingly.
Commun. Pure Appl. Math. 62 (2009), no 8, pp. 999-1032 Published version
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How hot can a heat bath get?
Commun. Math. Phys. 292 (2009), no 1, pp. 131-177 Published version
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A simple framework to justify linear response theory
Written in collaboration with A. J. Majda.
Nonlinearity 23 (2010), no 4, pp. 909-922 Published version
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A chain of interacting particles under strain
Written in collaboration with M. Allman and V. Betz.
Stoch. Proc. Appl. 121 (2011), no 9, pp. 2014-2042 Published version
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Markov processes

Yet another look at Harris' ergodic theorem for Markov chains
Written in collaboration with J. Mattingly.
Seminar on Stochastic Analysis, Random Fields and Applications VI, Progr. Probab. 63 (2011), pp. 109–117
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Stationary distributions for diffusions with inert drift
Written in collaboration with R. Bass, K. Burdzy, and Z.-Q. Chen.
Prob. Theory Rel. Fields 146 (2010), no 1, pp. 1-47 Published version
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Non-asymptotic mixing of the MALA algorithm
Written in collaboration with N. Bou-Rabee.
IMA Jour. Num. Anal. 33 (2013), pp. 80-110 Published version
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On Malliavin's proof of Hörmander's theorem
Bull. Sci. Math. 135 (2011), no 6-7, pp. 650-666 Published version
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Spectral Gaps for a Metropolis-Hastings Algorithm in Infinite Dimensions
Written in collaboration with A. Stuart and S. Vollmer.
Preprint, 2010 (to appear in Ann. Appl. Probab.)
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Improved Diffusion Monte Carlo
Written in collaboration with J. Weare.
Preprint, 2012 (to appear in Commun. Pure Appl. Math.)
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The Brownian Fan
Written in collaboration with J. Weare.
Preprint, 2012 (to appear in Commun. Pure Appl. Math.)
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Exponential ergodicity for Markov processes with random switching
Written in collaboration with B. Cloez.
Preprint, 2013 (to appear in Bernoulli)
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Non-Markovian Processes

Ergodicity of stochastic differential equations driven by fractional Brownian motion
Ann. Probab. 33 (2005), no 3, pp. 703-758 Published version
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Ergodic theory for SDEs with extrinsic memory
Written in collaboration with A. Ohashi
Ann. Probab. 35 (2007), no 5, pp. 1950-1977 Published version
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A version of Hörmander's theorem for the fractional Brownian motion
Written in collaboration with F. Baudoin
Prob. Theory Rel. Fields 139 (2007), no 3-4, pp. 373-395 Published version
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Ergodic properties of a class of non-Markovian processes
in Trends in Stochastic Analysis, LMS Lecture Notes Series 353, pp. 65-98
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Asymptotic coupling and a weak form of Harris' theorem with applications to stochastic delay equations
Written in collaboration with J. Mattingly and M. Scheutzow.
Prob. Theory Rel. Fields 149 (2011), no 1, p. 223 Published version
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Ergodicity of hypoelliptic SDEs driven by fractional Brownian motion
Written in collaboration with N. S. Pillai.
Annals of IHP 47 (2011), no 2, pp. 601-628 Published version
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Regularity of Laws and Ergodicity of Hypoelliptic SDEs Driven by Rough Paths
Written in collaboration with N. S. Pillai.
Ann. Probab. 41 (2013), no 4, pp. 2544-2598 Published version
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Smoothness of the density for solutions to Gaussian rough differential equations
Written in collaboration with T. Cass, C. Litterer and S. Tindel.
Ann. Probab. 43 (2015), no 1, pp. 188-239 Published version
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Stochastic Differential Equations

Periodic Homogenization for Hypoelliptic Diffusions
Written in collaboration with G. Pavliotis
J. Stat. Phys. 117 (2004), no 1, pp. 261-279 Published version
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On the Controllability of Conservative Systems
Unpublished Note, 2005
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Homogenization of periodic linear degenerate PDEs
Written in collaboration with E. Pardoux
J. Funct. Anal. 255 (2008), no 9, pp. 2462--2487 Published version
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From ballistic to diffusive behavior in periodic potentials
Written in collaboration with G. Pavliotis
J. Stat. Phys. 131 (2008), no 1, pp. 175-202 Published version
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Ornstein-Uhlenbeck Processes on Lie Groups
Written in collaboration with J. Teichmann and F. Baudoin
J. Funct. Anal. 255 (2008), no 4, pp. 877-890 Published version
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Periodic homogenization with an interface: the one-dimensional case
Written in collaboration with C. Manson
Stoch. Proc. Appl. 120 (2010), no 8, pp. 1589-1605 Published version
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Periodic homogenization with an interface: the multi-dimensional case
Written in collaboration with C. Manson
Ann. Probab. 39 (2011), no 2, pp. 648-682 Published version
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Periodic homogenization with an interface
Written in collaboration with C. Manson
Proceedings of ISAAC 09 (2009)
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Loss of regularity for Kolmogorov equations
Written in collaboration with M. Hutzenthaler and A. Jentzen.
Preprint (2012)
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Geometric versus non-geometric rough paths
Written in collaboration with D. Kelly.
Preprint (2013)
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Implementation of Numerical Algorithms

GniCodes - Matlab programs for geometric numerical integration.
Written in collaboration with E. Hairer.
Frontiers in Numerical Analysis (Durham 2002), 199--240, Springer, Berlin, 2003.
The Matlab codes can be downloaded by clicking on this link
The Fortran codes can be downloaded by clicking on this link
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Short notes

Ergodic theory for infinite-dimensional stochastic processes.
To be published in Oberwolfach Reports, 2008.
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