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diff --git a/main.bib b/main.bib new file mode 100755 index 0000000..5a0439c --- /dev/null +++ b/main.bib @@ -0,0 +1,437 @@ +@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}, +} + + |