Publications by Nils Berglund

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Preprints

  1. With Baptiste Bergeot and Israa Zogheib:
    The dynamic saddle-node bifurcation with noise on the slow variable
    37 pages (2025)
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  2. With Tom Klose and Nikolas Tapia:
    Perturbative renormalisation of the Φ44-ε model via generalized Wick maps
    29 pages (2025)
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  3. Long-time dynamics of stochastic differential equations
    58 pages (2021)
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    Lecture notes, Summer School "From kinetic equations to statistical mechanics", June-July 2021

Monographs

 
 

Overview papers (peer reviewed)

  1. With Tom Klose
    Perturbation theory for the Φ43 measure, revisited with Hopf algebras
    23 pages (2022)
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    Proceedings of the conference Higher Structures Emerging from Renormalisation, Vienna, November 2022

  2. Noise-induced phase slips, log-periodic oscillations, and the Gumbel distribution
    Markov Processes Relat. Fields 22:467-505 (2016)
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    Proceedings of Inhomogeneous Random Systems, Institut Henri Poincaré, Paris, January 2014

  3. Kramers' law: Validity, derivations and generalisations
    Markov Processes Relat. Fields 19:459-490 (2013)
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    Proceedings of Inhomogeneous Random Systems, Institut Henri Poincaré, Paris, January 2011

  4. With Barbara Gentz:
    Metastability in simple climate models: Pathwise analysis of slowly driven Langevin equations
    Stoch. Dyn. 2:327-356 (2002)
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    Proceedings of the Second Workshop on Stochastic Climate Models, Chorin, Germany, July 2001

Papers

  1. With Georgi Medvedev and Gideon Simpson:
    Metastability in the stochastic nearest-neighbor Kuramoto model of coupled phase oscillators
    Nonlinearity 38:095031 (2025)
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  2. With Alexandra Blessing (Neamțu):
    Concentration estimates for SPDEs driven by fractional Brownian motion
    Electron. Commun. Probab. 30:1-13 (2025)
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  3. Reducing metastable continuous-space Markov chains to Markov chains on a finite set
    Annales de l'Institut Henri Poincaré Probab. Statist. 61:2036-2073 (2025)
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  4. With Yvain Bruned:
    BPHZ renormalisation and vanishing subcriticality asymptotics of the fractional Φ3d model
    Stochastics and Partial Differential Equations: Analysis and Computations 13:243-307 (2025)
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  5. With Rita Nader:
    Concentration estimates for slowly time-dependent singular SPDEs on the two-dimensional torus
    Electronic J. Probability 29:1-35 (2024)
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  6. With Rita Nader:
    Stochastic resonance in stochastic PDEs
    Stochastics and Partial Differential Equations: Analysis and Computations, 11:348-387 (2023)
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  7. With Christian Kuehn, Christian Bick, Maximilian Engel, Tobias Hurth, Annalisa Iuorio, and Cinzia Soresina:
    A General View on Double Limits in Differential Equations
    Physica D 431:133105 (2022)
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  8. An Eyring-Kramers law for slowly oscillating bistable diffusions
    Probability and Mathematical Physics 2-4:685-743 (2021)
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  9. With Christian Kuehn:
    Corrigendum to "Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions"
    Electronic J. Probability 24 (113):1-22 (2019)
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  10. With Manon Baudel:
    Spectral theory for random Poincaré maps
    SIAM J. Math. Analysis 49(6): 4319-4375 (2017)
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  11. With Christian Kuehn:
    Model Spaces of Regularity Structures for Space-Fractional SPDEs
    J. Statist. Phys. 168 (2):331-368 (2017)
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  12. With Giacomo Di Gesù and Hendrik Weber:
    An Eyring-Kramers law for the stochastic Allen-Cahn equation in dimension two
    Electronic J. Probability 22 (41):1-27 (2017)
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  13. With Christian Kuehn:
    Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions
    Electronic J. Probability 21 (18):1-48 (2016)
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  14. With Sébastien Dutercq:
    Interface dynamics of a metastable mass-conserving spatially extended diffusion
    J. Statist. Phys. 162 (1):334-370 (2016)
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  15. With Sébastien Dutercq:
    The Eyring-Kramers law for Markovian jump processes with symmetries
    J. Theoretical Probability, 29 (4):1240-1279 (2016)
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  16. With Barbara Gentz and Christian Kuehn:
    From random Poincaré maps to stochastic mixed-mode-oscillation patterns
    J. Dynamics Differential Equations 27 (1):83-136 (2015)
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  17. With Barbara Gentz:
    On the noise-induced passage through an unstable periodic orbit II: General case
    SIAM J. Math. Anal. 46 (1):310-352 (2014)
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  18. With Barbara Gentz:
    Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond
    Electronic J. Probability 18 (24):1-58 (2013)
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  19. With Damien Landon:
    Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh-Nagumo model
    Nonlinearity 25:2303-2335 (2012)
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  20. With Barbara Gentz and Christian Kuehn:
    Hunting French Ducks in a Noisy Environment
    J. Differential Equations 252:4786-4841 (2012)
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  21. With Barbara Gentz:
    The Eyring-Kramers law for potentials with nonquadratic saddles
    Markov Processes Relat. Fields 16:549-598 (2010)
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  22. With Barbara Gentz:
    Anomalous behavior of the Kramers rate at bifurcations in classical field theories
    J. Phys. A: Math. Theor. 42:052001 (2009)
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  23. With Jean-Philippe Aguilar:
    The effect of classical noise on a quantum two-level system
    J. Math. Phys. 49:102102 (23 pp) (2008)
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  24. With Bastien Fernandez and Barbara Gentz:
    Metastability in interacting nonlinear stochastic differential equations II: Large-N behaviour
    Nonlinearity 20:2583-2614 (2007)
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  25. With Bastien Fernandez and Barbara Gentz:
    Metastability in interacting nonlinear stochastic differential equations I: From weak coupling to synchronisation
    Nonlinearity 20:2551-2581 (2007)
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  26. With Barbara Gentz:
    Universality of first-passage and residence-time distributions in non-adiabatic stochastic resonance
    Europhys. Letters 70:1-7 (2005)
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  27. With Barbara Gentz:
    On the noise-induced passage through an unstable periodic orbit I: Two-level model
    J. Statist. Phys. 114:1577-1618 (2004)
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  28. With Barbara Gentz:
    Geometric singular perturbation theory for stochastic differential equations
    J. Differential Equations 191:1-54 (2003)
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  29. With Barbara Gentz:
    Beyond the Fokker-Planck equation: Pathwise control of noisy bistable systems
    J. Phys. A 35:2057-2091 (2002)
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  30. With Barbara Gentz:
    The effect of additive noise on dynamical hysteresis
    Nonlinearity 15:605-632 (2002)
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  31. With Barbara Gentz:
    A sample-paths approach to noise-induced synchronization: Stochastic resonance in a double-well potential
    Ann. Appl. Probab. 12:1419-1470 (2002)
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  32. With Barbara Gentz:
    Pathwise description of dynamic pitchfork bifurcations with additive noise
    Probab. Theory Related Fields 122:341-388 (2002)
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  33. With Turgay Uzer:
    The averaged dynamics of the hydrogen atom in crossed electric and magnetic fields as a perturbed Kepler problem
    Found. Phys. 31:283-326 (2001)
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  34. Control of dynamic Hopf bifurcations
    Nonlinearity 13:225-248 (2000)
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  35. With Hervé Kunz:
    Memory Effects and Scaling Laws in Slowly Driven Systems
    J. Phys. A 32:15-39 (1999)
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  36. With Hervé Kunz:
    Chaotic Hysteresis in an Adiabatically Oscillating Double Well
    Phys. Rev. Letters 78:1691-1694 (1997)
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  37. With Alex Hansen, Eivind H. Hauge and Jarosław Piasecki:
    Can a Local Repulsive Potential Trap an Electron?
    Phys. Rev. Letters 77:2149-2153 (1996)
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  38. With Hervé Kunz:
    Integrability and Ergodicity of Classical Billiards in a Magnetic Field
    J. Stat. Phys 83:81-126 (1996)
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Book chapters

  1. With Barbara Gentz:
    Stochastic dynamic bifurcations and excitability
    in C. Laing and G. Lord, (Eds.), Stochastic methods in Neuroscience, p. 65-93, Oxford University Press (2009)
    Publisher's site, (draft version), , ,

  2. With Klaus R. Schneider:
    Control of dynamic bifurcations
    in D. Aeyels, F. Lamnabhi-Lagarrigue, A. van der Schaft (Eds.) Stability and Stabilization of Nonlinear Systems, Lecture Notes in Contr. and Inform. Sciences 246 (Springer, Berlin, 1999)
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    Proceedings of the 1st NCN-workshop, Ghent, Belgium, March 1999

  3. Bifurcations, scaling laws and hysteresis in singularly perturbed systems
    in B. Fiedler, K. Gröger, J. Sprekels (Eds.) Equadiff '99 (World Scientific, Singapore, 2000)
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    Proceedings of the conference Equadiff '99, Berlin, Germany, August 1999

Other proceedings

  1. Stochastic dynamical systems in neuroscience
    Oberwolfach Reports 8:2290-2293 (2011)
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    Proceedings of the miniworkshop Dynamics of Stochastic Systems and their Approximation, Oberwolfach, Germany, August 2011

  2. Dynamic bifurcations: hysteresis, scaling laws and feedback control
    Prog. Theor. Phys. Suppl. 139:325-336 (2000)
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    Proceedings of the 4th conference Let's face chaos through nonlinear dynamics, Maribor, Slovenia, June/July 1999

  3. Classical Billiards in a Magnetic Field and a Potential
    Nonlinear Phenomena in Complex Systems 3:61-70 (2000)
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    Proceedings of the 3rd conference Let's face chaos through nonlinear dynamics, Maribor, Slovenia, June/July 1996

  4. On the Reduction of Adiabatic Dynamical Systems near Equilibrium Curves
    , mp-arc/98-574
    Proceedings of the conference Celestial Mechanics, Separatrix Splitting, Diffusion, Aussois, France, June 1998

Outreach and popularisation

  1. Metastability of Stochastic Partial Differential Equations and Fredholm Determinants
    EMS Newsletter 117, 6-14, EMS, 2020
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  2. Métastabilité d'EDP stochastiques et déterminants de Fredholm
    Gazette des Mathématiciens 163, 14-25, SMF, 2020
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  3. Mayonnaise et élections américaines
    Dossier Pour La Science, 2016

  4. Des ondes dans mon billard
    Images des Mathématiques, CNRS, 2020

  5. Modèles simples du climat [Part1, Part 2, Part 3]
    Images des Mathématiques, CNRS, 2020

  6. 1951 : Le calcul d'Itō
    Images des Mathématiques, CNRS, 2020

  7. 1952 : L'algorithme de Metropolis
    Images des Mathématiques, CNRS, 2020

  8. Résoudre des équations en comptant des arbres
    Images des Mathématiques, CNRS, 2018

  9. Les diagrammes de Feynman [Part1, Part2, Part3]
    Images des Mathématiques, CNRS, 2016

  10. Probabiliser
    Images des Mathématiques, CNRS, 2015

  11. Des canards dans mes neurones
    Images des Mathématiques, CNRS, 2015

  12. Qu'est-ce qu'une Équation aux Dérivées Partielles Stochastique ?
    Images des Mathématiques, CNRS, 2014

  13. Notre univers est-il irréversible ?
    Images des Mathématiques, CNRS, 2013

  14. La probabilité d'extinction d'une espèce menacée
    Images des Mathématiques, CNRS, 2013

  15. Rangez-moi ces bouquins !
    Images des Mathématiques, CNRS, 2012

  16. Hasard et glaciations
    Mathématiques de la Planète Terre, 2013
    Also published in Brèves de Maths, Nouveau Monde, 2014

  17. Le climat et ses aléas
    Microscoop CNRS, Hors-série 22, 2013

  18. Les mathématiques à la rescousse de la physique quantique — et inversement
    Fenêtre sur Sciences, Lycée Dessaignes Blois, December 2019

  19. Modèles aléatoires en biologie
    Les mardis de la science, March 2016

  20. Mathématiques du quotidien
    Fête de la Science, October 2014

  21. Connaissez-vous les nombres réels ?
    Centre Galois, June 2025

  22. Combien de lampes pour éclairer un labyrinthe de miroirs ?
    Centre Galois, June 2023

  23. Comment obtenir des résultats certains grâce aux probabilités ?
    Centre Galois, June 2021

  24. Résoudre des équations par le dessin
    Centre Galois, June 2018
    Version of June 2019

  25. Mathématiques et biologie
    Centre Galois, June 2014

  26. Probabilités et physique statistique
    Centre Galois, June 2011
    Version of June 2013

  27. Récréation mathématique: La suite de Fibonacci
    USTV, November 2005

Theses

Lecture notes

  1. Processus aléatoires et applications — Algorithmes MCMC et vitesse de convergence
    Orléans, December 2024
    ,

  2. An introduction to singular stochastic PDEs: Allen-Cahn equations, metastability and regularity structures
    Sarajevo, January 2019

  3. Probabilités et statistiques
    Orléans, March 2010

  4. Martingales et calcul stochastique
    Orléans, November 2009
    ,

  5. Processus aléatoires et applications
    Orléans, November 2009
    ,
    Croatian translation (by Tomislav Doslic)

  6. Théorie des probabilités
    USTV, October 2005

  7. Introduction aux équations différentielles stochastiques
    CPT, January 2005

  8. Introduction à l'intégration stochastique
    UTV, October 2003

  9. Perturbation theory of dynamical systems
    ETH, Summer semester 2001

  10. Geometrical theory of dynamical systems
    ETH, Winter semester 2000-2001