path: root/main.bib

@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},
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  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},
    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)"
}

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    Publisher = {American Physical Society},
}

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}

@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},
}

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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},
}

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MRREVIEWER = {Yves Derriennic},
       DOI = {10.1007/BF00531822},
       URL = {https://doi-org.extranet.enpc.fr/10.1007/BF00531822},
}