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+@ARTICLE{2019arXiv190405973G,
+       author = {{Gomes}, S.~N. and {Pavliotis}, G.~A. and {Vaes}, U.},
+        title = "{Mean-field limits for interacting diffusions with colored noise: phase transitions and spectral numerical methods}",
+      journal = {arXiv e-prints},
+     keywords = {Mathematics - Numerical Analysis, Condensed Matter - Statistical Mechanics, 35Q70, 35Q83, 35Q84, 65N35, 65M70, 82B26},
+         year = "2019",
+        month = "Apr",
+   commenteid = {arXiv:1904.05973},
+ commentpages = {arXiv:1904.05973},
+archivePrefix = {arXiv},
+       eprint = {1904.05973},
+ primaryClass = {math.NA},
+       adsurl = {https://ui.adsabs.harvard.edu/abs/2019arXiv190405973G},
+      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
+}
+
+@article {abdulle2017spectral,
+    AUTHOR = {Abdulle, A. and Pavliotis, G. A. and Vaes, U.},
+    TITLE = {Spectral methods for multiscale stochastic differential equations},
+    JOURNAL = {SIAM/ASA J. Uncertain. Quantif.},
+    FJOURNAL = {SIAM/ASA Journal on Uncertainty Quantification},
+    VOLUME = {5},
+    YEAR = {2017},
+    NUMBER = {1},
+    PAGES = {720--761},
+}
+
+
+@article {paper_gle,
+    AUTHOR = {Pavliotis, G. A. and Vaes, U.},
+    TITLE = {Effective diffusion for the generalized {L}angevin equation in a periodic potential},
+    YEAR = {2019, in preparation},
+}
+
+@article {MR3390380,
+    AUTHOR = {Mohammadi, Masoumeh and Borzi, Alfio},
+     TITLE = {A {H}ermite spectral method for a {F}okker-{P}lanck optimal
+              control problem in an unbounded domain},
+   JOURNAL = {Int. J. Uncertain. Quantif.},
+  FJOURNAL = {International Journal for Uncertainty Quantification},
+    VOLUME = {5},
+      YEAR = {2015},
+    NUMBER = {3},
+     PAGES = {233--254},
+      ISSN = {2152-5080},
+   MRCLASS = {65M70 (49K20 49M05 60H30)},
+  MRNUMBER = {3390380},
+MRREVIEWER = {Brian Bradie},
+COMMENTDOI = {10.1615/Int.J.UncertaintyQuantification.2015010310},
+}
+
+@article {MR2966923,
+    AUTHOR = {Annunziato, M. and Borz\`\i , A.},
+     TITLE = {A {F}okker-{P}lanck control framework for multidimensional
+              stochastic processes},
+   JOURNAL = {J. Comput. Appl. Math.},
+  FJOURNAL = {Journal of Computational and Applied Mathematics},
+    VOLUME = {237},
+      YEAR = {2013},
+    NUMBER = {1},
+     PAGES = {487--507},
+      ISSN = {0377-0427},
+   MRCLASS = {49K45 (60H10 65M55 93C20)},
+  MRNUMBER = {2966923},
+       COMMENTDOI = {10.1016/j.cam.2012.06.019},
+       COMMENTURL = {https://doi.org/10.1016/j.cam.2012.06.019},
+}
+
+@article {MR967848,
+    AUTHOR = {Barzilai, Jonathan and Borwein, Jonathan M.},
+     TITLE = {Two-point step size gradient methods},
+   JOURNAL = {IMA J. Numer. Anal.},
+  FJOURNAL = {IMA Journal of Numerical Analysis},
+    VOLUME = {8},
+      YEAR = {1988},
+    NUMBER = {1},
+     PAGES = {141--148},
+      ISSN = {0272-4979},
+   MRCLASS = {65K05},
+  MRNUMBER = {967848},
+       DOI = {10.1093/imanum/8.1.141},
+       URL = {https://doi.org/10.1093/imanum/8.1.141},
+}
+
+@article {MR2793823,
+    AUTHOR = {Ottobre, M. and Pavliotis, G. A.},
+     TITLE = {Asymptotic analysis for the generalized {L}angevin equation},
+   JOURNAL = {Nonlinearity},
+  FJOURNAL = {Nonlinearity},
+    VOLUME = {24},
+      YEAR = {2011},
+    NUMBER = {5},
+     PAGES = {1629--1653},
+      ISSN = {0951-7715},
+   MRCLASS = {60H10 (35H10 35R60 60F17 60J60 82C31)},
+  MRNUMBER = {2793823},
+MRREVIEWER = {Dora Sele\v{s}i},
+       COMMENTDOI = {10.1088/0951-7715/24/5/013},
+       COMMENTURL = {https://doi.org/10.1088/0951-7715/24/5/013},
+}
+
+@article{roussel2018spectral,
+  title={Spectral methods for {L}angevin dynamics and associated error estimates},
+  commentauthor={Roussel, Julien and Stoltz, Gabriel},
+  author={Roussel, J. and Stoltz, G.},
+  commentjournal={ESAIM: Mathematical Modelling and Numerical Analysis},
+  journal={ESAIM: Math. Model. Numer. Anal.},
+  volume={52},
+  number={3},
+  pages={1051--1083},
+  year={2018},
+  publisher={EDP Sciences}
+}
+
+@article {MR3509213,
+    AUTHOR = {Leli\`evre, T. and Stoltz, G.},
+     TITLE = {Partial differential equations and stochastic methods in
+              molecular dynamics},
+   JOURNAL = {Acta Numer.},
+  FJOURNAL = {Acta Numerica},
+    VOLUME = {25},
+      YEAR = {2016},
+     PAGES = {681--880},
+}
+
+@article {hairer2004periodic,
+    AUTHOR = {Hairer, M. and Pavliotis, G. A.},
+     TITLE = {Periodic homogenization for hypoelliptic diffusions},
+   JOURNAL = {J. Statist. Phys.},
+  FJOURNAL = {Journal of Statistical Physics},
+    VOLUME = {117},
+      YEAR = {2004},
+    NUMBER = {1-2},
+     PAGES = {261--279},
+      ISSN = {0022-4715},
+   MRCLASS = {82C31},
+  MRNUMBER = {2098568},
+MRREVIEWER = {Luc Rey-Bellet},
+}
+
+@book {pavliotis2011applied,
+    AUTHOR = {Pavliotis, G. A.},
+    TITLE = {Stochastic processes and applications},
+    SERIES = {Texts in Applied Mathematics},
+    VOLUME = {60},
+    NOTE = {Diffusion processes, the Fokker-Planck and Langevin equations},
+    PUBLISHER = {Springer, New York},
+    YEAR = {2014},
+    PAGES = {xiv+339},
+}
+
+@article {MR2562709,
+    AUTHOR = {Villani, C\'{e}dric},
+     TITLE = {Hypocoercivity},
+   JOURNAL = {Mem. Amer. Math. Soc.},
+  FJOURNAL = {Memoirs of the American Mathematical Society},
+    VOLUME = {202},
+      YEAR = {2009},
+    NUMBER = {950},
+     PAGES = {iv+141},
+      ISSN = {0065-9266},
+      ISBN = {978-0-8218-4498-4},
+   MRCLASS = {35Q84 (35H10 76N10 76P05 82C70)},
+  MRNUMBER = {2562709},
+MRREVIEWER = {Andr\'{a}s Domokos},
+       DOI = {10.1090/S0065-9266-09-00567-5},
+       URL = {https://doi.org/10.1090/S0065-9266-09-00567-5},
+}
+
+@article {MR3324910,
+    AUTHOR = {Dolbeault, Jean and Mouhot, Cl\'{e}ment and Schmeiser, Christian},
+     TITLE = {Hypocoercivity for linear kinetic equations conserving mass},
+   JOURNAL = {Trans. Amer. Math. Soc.},
+  FJOURNAL = {Transactions of the American Mathematical Society},
+    VOLUME = {367},
+      YEAR = {2015},
+    NUMBER = {6},
+     PAGES = {3807--3828},
+      ISSN = {0002-9947},
+   MRCLASS = {35F10 (35B40 35H10 82C31)},
+  MRNUMBER = {3324910},
+MRREVIEWER = {Ingrid Alma Belti\c{t}\u{a}},
+       DOI = {10.1090/S0002-9947-2015-06012-7},
+       URL = {https://doi.org/10.1090/S0002-9947-2015-06012-7},
+}
+
+@article {MR2576899,
+    AUTHOR = {Dolbeault, Jean and Mouhot, Cl\'{e}ment and Schmeiser, Christian},
+     TITLE = {Hypocoercivity for kinetic equations with linear relaxation
+              terms},
+   JOURNAL = {C. R. Math. Acad. Sci. Paris},
+  FJOURNAL = {Comptes Rendus Math\'{e}matique. Acad\'{e}mie des Sciences. Paris},
+    VOLUME = {347},
+      YEAR = {2009},
+    NUMBER = {9-10},
+     PAGES = {511--516},
+      ISSN = {1631-073X},
+   MRCLASS = {35F20 (82C40)},
+  MRNUMBER = {2576899},
+       DOI = {10.1016/j.crma.2009.02.025},
+       URL = {https://doi.org/10.1016/j.crma.2009.02.025},
+}
+
+@ARTICLE{2018arXiv180804299D,
+       author = {{Deligiannidis}, George and {Paulin}, Daniel and
+         {Bouchard-C{\^o}t{\'e}}, Alexandre and {Doucet}, Arnaud},
+        title = "{Randomized Hamiltonian Monte Carlo as Scaling Limit of the Bouncy Particle Sampler and Dimension-Free Convergence Rates}",
+      journal = {arXiv e-prints},
+     keywords = {Statistics - Computation, Mathematics - Probability},
+         year = "2018",
+        month = "Aug",
+        pages = {arXiv:1808.04299},
+archivePrefix = {arXiv},
+       eprint = {1808.04299},
+ primaryClass = {stat.CO},
+       adsurl = {https://ui.adsabs.harvard.edu/abs/2018arXiv180804299D},
+      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
+}
+
+@article {MR2294477,
+    AUTHOR = {H\'{e}rau, Fr\'{e}d\'{e}ric},
+     TITLE = {Short and long time behavior of the {F}okker-{P}lanck equation
+              in a confining potential and applications},
+   JOURNAL = {J. Funct. Anal.},
+  FJOURNAL = {Journal of Functional Analysis},
+    VOLUME = {244},
+      YEAR = {2007},
+    NUMBER = {1},
+     PAGES = {95--118},
+      ISSN = {0022-1236},
+   MRCLASS = {47D06 (35B40 35K55 82C05)},
+  MRNUMBER = {2294477},
+MRREVIEWER = {Silvia Totaro},
+       DOI = {10.1016/j.jfa.2006.11.013},
+       URL = {https://doi.org/10.1016/j.jfa.2006.11.013},
+}
+
+@article {MR3262508,
+    AUTHOR = {Hairer, Martin and Stuart, Andrew M. and Vollmer, Sebastian
+              J.},
+     TITLE = {Spectral gaps for a {M}etropolis-{H}astings algorithm in
+              infinite dimensions},
+   JOURNAL = {Ann. Appl. Probab.},
+  FJOURNAL = {The Annals of Applied Probability},
+    VOLUME = {24},
+      YEAR = {2014},
+    NUMBER = {6},
+     PAGES = {2455--2490},
+      ISSN = {1050-5164},
+   MRCLASS = {60J22 (37A30 60B12 60J05 65C05 65C40)},
+  MRNUMBER = {3262508},
+MRREVIEWER = {Laurent Miclo},
+       DOI = {10.1214/13-AAP982},
+       URL = {https://doi.org/10.1214/13-AAP982},
+}
+
+@article {MR2427108,
+    AUTHOR = {Pavliotis, G. A. and Vogiannou, A.},
+     TITLE = {Diffusive transport in periodic potentials: underdamped
+              dynamics},
+   JOURNAL = {Fluct. Noise Lett.},
+  FJOURNAL = {Fluctuation and Noise Letters (FNL). An Interdisciplinary
+              Scientific Journal on Random Processes in Physical, Biological
+              and Technological Systems},
+    VOLUME = {8},
+      YEAR = {2008},
+    NUMBER = {2},
+     PAGES = {L155--L173},
+      ISSN = {0219-4775},
+   MRCLASS = {82C41 (60J65 82C44)},
+  MRNUMBER = {2427108},
+       DOI = {10.1142/S0219477508004453},
+       URL = {https://doi.org/10.1142/S0219477508004453},
+}
+
+@article {MR1941990,
+    AUTHOR = {Metafune, G. and Pallara, D. and Priola, E.},
+     TITLE = {Spectrum of {O}rnstein-{U}hlenbeck operators in {$L^p$} spaces
+              with respect to invariant measures},
+   JOURNAL = {J. Funct. Anal.},
+  FJOURNAL = {Journal of Functional Analysis},
+    VOLUME = {196},
+      YEAR = {2002},
+    NUMBER = {1},
+     PAGES = {40--60},
+      ISSN = {0022-1236},
+   MRCLASS = {47D07},
+  MRNUMBER = {1941990},
+MRREVIEWER = {Vladimir I. Bogachev},
+       DOI = {10.1006/jfan.2002.3978},
+       URL = {https://doi.org/10.1006/jfan.2002.3978},
+}
+
+@Article{Kopec2015,
+author="Kopec, Marie",
+title="Weak backward error analysis for {L}angevin process",
+journal="BIT Numer. Math.",
+year="2015",
+month="Dec",
+day="01",
+volume="55",
+number="4",
+pages="1057--1103",
+abstract="We consider numerical approximations of stochastic Langevin equations by implicit methods. We show a weak backward error analysis result in the sense that the generator associated with the numerical solution coincides with the solution of a modified Kolmogorov equation up to high order terms with respect to the stepsize. This implies that every measure of the numerical scheme is close to a modified invariant measure obtained by asymptotic expansion. Moreover, we prove that, up to negligible terms, the dynamics associated with the considered implicit scheme is exponentially mixing: The law of the scheme converges exponentially fast to a constant up to an error that we can optimize.",
+issn="1572-9125",
+doi="10.1007/s10543-015-0546-0",
+url="https://doi.org/10.1007/s10543-015-0546-0"
+}
+
+@article {MR2394704,
+    AUTHOR = {Hairer, M. and Pavliotis, G. A.},
+     TITLE = {From ballistic to diffusive behavior in periodic potentials},
+   JOURNAL = {J. Stat. Phys.},
+  FJOURNAL = {Journal of Statistical Physics},
+    VOLUME = {131},
+      YEAR = {2008},
+    NUMBER = {1},
+     PAGES = {175--202},
+      ISSN = {0022-4715},
+   MRCLASS = {82C31 (37H10 60H10 82C80)},
+  MRNUMBER = {2394704},
+MRREVIEWER = {Kiyomasa Narita},
+       COMMENTDOI = {10.1007/s10955-008-9493-3},
+       COMMENTURL = {https://doi.org/10.1007/s10955-008-9493-3},
+}
+
+@article {GPGSUV_2020,
+    AUTHOR = {Pavliotis, G. A. and Stoltz, G. and Vaes, U.},
+     TITLE = {Scaling limits for the generalized {L}angevin equation},
+   JOURNAL = {J. Nonlinear Sci.},
+  FJOURNAL = {Journal of Nonlinear Science},
+    VOLUME = {31},
+      YEAR = {2021},
+    NUMBER = {1},
+     PAGES = {Paper No. 8},
+      ISSN = {0938-8974},
+   MRCLASS = {Prelim},
+  MRNUMBER = {4195749},
+       DOI = {10.1007/s00332-020-09671-4},
+       URL = {https://doi-org.extranet.enpc.fr/10.1007/s00332-020-09671-4},
+}
+
+@book {pavliotis2008multiscale,
+    AUTHOR = {Pavliotis, G. A. and Stuart, A. M.},
+    TITLE = {Multiscale methods},
+    SERIES = {Texts in Applied Mathematics},
+    VOLUME = {53},
+    NOTE = {Averaging and homogenization},
+    PUBLISHER = {Springer, New York},
+    YEAR = {2008},
+    PAGES = {xviii+307},
+    ISBN = {978-0-387-73828-4},
+    MRCLASS = {60-02 (34E13 35R60 60H10 74Q05 76M50)},
+    MRNUMBER = {2382139},
+    MRREVIEWER = {Bogdan Iftimie},
+}
+
+@ARTICLE{2022arXiv220609781P,
+    author = {{Pavliotis}, G.~A. and {Stoltz}, G. and {Vaes}, U.},
+    title = "{Mobility estimation for Langevin dynamics using control variates}",
+    journal = {arXiv preprint},
+    year = 2022,
+    volume = {2206.09781},
+    adsurl = {https://ui.adsabs.harvard.edu/abs/2022arXiv220609781P},
+    adsnote = {Provided by the SAO/NASA Astrophysics Data System},
+    % note = "(Submitted)"
+}
+
+@Article{Braun02,
+    Title = {Role of long jumps in surface diffusion},
+    Author = {Braun, O. M. and Ferrando, R.},
+    Journal= {Phys. Rev. E},
+    Year = {2002},
+    Pages = {061107},
+    Volume = {65},
+    % Issue = {6},
+    Numpages = {11},
+    doi = {10.1103/PhysRevE.65.061107},
+    Publisher = {American Physical Society},
+}
+
+@article{chen1996surface,
+    title={Surface diffusion in the low-friction limit: {O}ccurrence of long jumps},
+    author={Chen, L. Y. and Baldan, M. R. and Ying, S. C.},
+    journal={Phys. Rev. B},
+    volume={54},
+    number={12},
+    pages={8856},
+    year={1996},
+    doi={10.1103/PhysRevB.54.8856},
+    publisher={APS}
+}
+
+@phdthesis{roussel_thesis,
+    title={Theoretical and Numerical Analysis of Non-Reversible Dynamics in Computational Statistical Physics},
+    author={Julien Roussel},
+    year={2018},
+    school={Université Paris-Est},
+}
+
+@article {MR885138,
+    AUTHOR = {Kliemann, W.},
+     TITLE = {Recurrence and invariant measures for degenerate diffusions},
+   JOURNAL = {Ann. Probab.},
+  FJOURNAL = {The Annals of Probability},
+    VOLUME = {15},
+      YEAR = {1987},
+    NUMBER = {2},
+     PAGES = {690--707},
+      ISSN = {0091-1798},
+   MRCLASS = {58G32 (60J60)},
+  MRNUMBER = {885138},
+MRREVIEWER = {Uwe R\"{o}sler},
+       URL =
+              {http://links.jstor.org.extranet.enpc.fr/sici?sici=0091-1798(198704)15:2<690:RAIMFD>2.0.CO;2-Z&origin=MSN},
+}
+
+@article {MR663900,
+    AUTHOR = {Bhattacharya, R. N.},
+     TITLE = {On the functional central limit theorem and the law of the
+              iterated logarithm for {M}arkov processes},
+   JOURNAL = {Z. Wahrsch. Verw. Gebiete},
+  FJOURNAL = {Zeitschrift f\"{u}r Wahrscheinlichkeitstheorie und Verwandte
+              Gebiete},
+    VOLUME = {60},
+      YEAR = {1982},
+    NUMBER = {2},
+     PAGES = {185--201},
+      ISSN = {0044-3719},
+   MRCLASS = {60J25 (60F17)},
+  MRNUMBER = {663900},
+MRREVIEWER = {Yves Derriennic},
+       DOI = {10.1007/BF00531822},
+       URL = {https://doi-org.extranet.enpc.fr/10.1007/BF00531822},
+}
+
+