Research

My research focuses on the qualitative and quantitative analysis of complex dynamical systems arising in physics, chemistry, and engineering. I am particularly interested in understanding how macroscopic behavior emerges from microscopic or stochastic models, using tools from partial differential equations (PDEs), stochastic analysis, and variational methods.

A central theme in my work is the study of metastability and phase transitions in systems motivated by statistical mechanics and particle dynamics. This includes investigating how collective effects and noise lead to rich dynamical phenomena such as nucleation, coarsening, and metastable states. At the interface with stochastic analysis, I analyze many-particle limits of interacting systems and their continuum descriptions, often formulated as gradient flows in spaces of probability measures.

I am also interested in structure-preserving numerical schemes for nonlinear diffusion and aggregation equations, the long-time behavior of dissipative systems via entropy and functional inequalities, and variational convergence methods that connect discrete and continuous dynamics. My research extends to nonlocal and graph-based models, motivated both by physical systems and machine learning, where questions of dimension reduction and multi-scale dynamics naturally arise.

Keywords

  • Metastability and phase transitions in molecular dynamics and statistical mechanics
  • Nucleation, coarsening, and long-time asymptotics of complex systems
  • Variational methods for dissipative and gradient flow-type evolution equations
  • Entropy methods and functional inequalities (spectral gap, log-Sobolev)
  • Gradient flows and variational convergence; synthetic curvature and geodesic convexity
  • Quantitative error analysis and structure-preserving numerical schemes
  • Dimension reduction in multiscale dynamics (physics, chemistry, machine learning)
  • Discrete and nonlocal dynamics on graphs and data-driven structures
  • Convergence rates and stability of numerical approximation methods

Publications

Preprints submitted

  1. Alexander Mielke, André Schlichting, Artur Stephan. Derivation of the fourth-order DLSS equation with nonlinear mobility via chemical reactions. [ arXiv | pdf ]
  2. Chun Yin Lam, André Schlichting. Existence and Non-existence for Continuous Generalized Exchange-Driven Growth model. [ arXiv | pdf ]
  3. Chun Yin Lam, André Schlichting. Convergence of a Stochastic Particle System to the Continuous Generalized Exchange-Driven Growth Model. [ arXiv | pdf ]
  4. Daniel Matthes, Eva-Maria Rott, André Schlichting. Diffusive transport on the real line: semi-contractive gradient flows and their discretization. [ arXiv | pdf ]
  5. Anna Shalova, André Schlichting. Solutions of stationary McKean-Vlasov equation on a high-dimensional sphere and other Riemannian manifolds. [ arXiv | pdf ]
  6. Anna Shalova, André Schlichting, Mark Peletier. Singular-limit analysis of gradient descent with noise injection. [ arXiv | pdf | html ]
  7. Jasper Hoeksema, Chun Yin Lam, André Schlichting. Variational convergence for an irreversible exchange-driven stochastic particle system. [ arXiv | pdf ]

Peer reviewed

  1. Daniel Matthes, Eva-Maria Rott, Giuseppe Savaré, André Schlichting. A structure preserving discretization for the Derrida-Lebowitz-Speer-Spohn equation based on diffusive transport. Numerische Mathematik. [ doi | arXiv | pdf ]
  2. Ilka Budde, André Schlichting, David Ing, Sandra Schimmelpfennig, Joelle M-J Romac, Sandip M Swain, Rodger A. Liddle, Angela Stevens, Albrecht Schwab, Zoltán Pethő. Piezo1-induced durotaxis of pancreatic stellate cells depends on TRPC1 and TRPV4 channels. Journal of Cell Science, 138 (8), 2025. [ doi | bioRxiv | pdf-main, pdf-supp-info, pdf-supp-num ]
  3. Antonio Esposito, Georg Heinze, André Schlichting. Graph-to-local limit for the nonlocal interaction equation. J. Math. Pures Appl, 194, (2025), 103663. [ doi | arXiv | pdf ]
  4. Anastasiia Hraivoronska, André Schlichting, Oliver Tse. Variational convergence of the Scharfetter-Gummel scheme to the aggregation-diffusion equation and vanishing diffusion limit. Numer. Math. 156, 2221–2292 (2024). [ doi | arXiv | pdf ]
  5. Martin Burger, Franca Hoffmann, Daniel Matthes, Matthias Erbar, André Schlichting. Covariance-modulated optimal transport and gradient flows. Arch. Ration. Mech. Anal. 249, 7 (2025). [ doi | arXiv | pdf ]
  6. Antonio Esposito, Rishabh S. Gvalani, André Schlichting, Markus Schmidtchen, On a novel gradient flow structure for the aggregation equation. Calc. Var. & PDE, 63, 126 (2024). [ doi | arXiv | pdf ]
  7. Antonio Esposito, Francesco S. Patacchini, André Schlichting. On a Class of Nonlocal Continuity Equations on Graphs. Eur. J. Appl. Math, 35(1), 2024, pp. 109-126. [ doi | arXiv | pdf ]
  8. Víctor Navarro-Fernández, André Schlichting. Error estimates for a finite volume scheme for advection-diffusion equations with rough coefficients.
    ESAIM: M2AN, Vol. 57, No. 4, 2023. [ doi | arXiv | pdf ]
  9. Víctor Navarro-Fernández, André Schlichting, Christian Seis. Optimal stability estimates and a new uniqueness result for advection-diffusion equations. Pure appl. anal. Vol. 4 (2022), No. 3, 571–596. [ doi | link | arXiv | pdf ]
  10. Mark Peletier, André Schlichting. Cosh gradient systems and tilting. Nonlinear Analysis Volume 231, June 2023, 113094. [ doi | arXiv | pdf ]
  11. Georg Menz, André Schlichting, Wenpin Tang, Tianqi Wu. Ergodicity of the infinite swapping algorithm at low temperature. Stoch. Process. their Appl. 151, 2022. [ doi | arXiv | pdf ]
  12. Barbara Niethammer, Robert L. Pego, André Schlichting, Juan J. L. Velázquez. Oscillations in a Becker-Döring model with injection and depletion. SIAM Journal on Applied Mathematics. 82(4), 2022. [ doi | arXiv | pdf ]
  13. André Schlichting, Christian Seis. The Scharfetter-Gummel scheme for aggregation-diffusion equations. IMA Journal of Numerical Analysis. Volume 42, Issue 3, July 2022, Pages 2361–2402. [ doi | free access | arXiv | pdf ]
  14. Constantin Eichenberg, André Schlichting. Self-similar behavior of the exchange-driven growth model with product kernel. Commun. Partial. Differ. Equ. 46(3), 2021. [ doi | free access | arXiv | pdf ]
  15. Antonio Esposito, Francesco S. Patacchini, André Schlichting, Dejan Slepčev. Nonlocal-interaction equation on graphs: gradient flow structure and continuum limit. Archive for Rational Mechanics and Analysis, 240, 699–760(2021) [ doi | arXiv | pdf ]
  16. Rishabh S. Gvalani, André Schlichting. Barriers of the McKean-Vlasov energy via a mountain pass theorem in the space of probability measures. Journal for Functional Analysis, 279(11), 108720 (2020). [ doi | arXiv | pdf ]
  17. Matthias Erbar, Max Fathi, André Schlichting, Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces. ALEA – Latin American Journal of Probability and Mathematical Statistics, 17, 445-471 (2020). [ doi | arXiv | pdf ]
  18. André Schlichting. The exchange-driven growth model: basic properties and longtime behavior. Journal Nonlinear Science, 30, 793–830 (2020) [ link | doi | arXiv | pdf ]
  19. José A. Carrillo, Rishabh S. Gvalani, Grigorios A. Pavliotis, André Schlichting. Long-time behaviour and phase transitions for the McKean–Vlasov equation on the torus. Archive for Rational Mechanics and Analysis, 235, 635–690 (2020) [ link | doi | arXiv | pdf ]
  20. André Schlichting, Martin Slowik.  Poincaré and logarithmic Sobolev constants for metastable Markov chains via capacitary inequalities. Annals of Applied Probability, 29(6), 3438-3488 (2019) [ arXiv | doi | pdf ]
  21. André Schlichting. Poincaré and Log–Sobolev Inequalities for Mixtures. Entropy 2019, 21(1). [ doi | arXiv | pdf ]
  22. Joseph G. Conlon, André Schlichting. A non-local problem for the Fokker-Planck equation related to the Becker-Döring model. Discret. Contin. Dyn. Syst. 39-4, 2019. [ doi | arXiv | pdf ]
  23. Manh Hong Duong, Agnes Lamacz, Mark A. Peletier, André Schlichting, Upanshu Sharma. Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics. Nonlinearity 31(10), 2018. [ doi |  arXiv | pdf ]
  24. André Schlichting. Macroscopic limit of the Becker-Döring equation via gradient flows. ESAIM:COCV 25(22), 2019. [ doi | arXiv | pdf ]
  25. André Schlichting, Christian Seis.  Analysis of the implicit upwind finite volume scheme with rough coefficients. Numer. Math., 2017. [ doi | view only | arXiv | pdf ]
  26. Simon Eberle, Barbara Niethammer, André Schlichting. Gradient flow formulation and longtime behaviour of a constrained Fokker-Planck equation. Nonlinear Anal. 158C, 2017). [ doi | journal | arXiv| pdf ]
  27. André Schlichting, Christian Seis. Convergence rates for upwind schemes with rough
    coefficients. SIAM J. Numer. Anal. 55 (2), 812–840, 2017. [ doi | arXiv |pdf ]
  28. Matthias Erbar, Max Fathi, Vaios Laschos, André Schlichting. Gradient flow structure for McKean-Vlasov equations on discrete spaces. Discret. Contin. Dyn. Syst. 36, 2016. [ doi | arXiv | pdf ]
  29. Georg Menz, André Schlichting. Poincaré and logarithmic Sobolev inequalities by decomposition of the energy landscape. Ann. Probab. 42(5), 2014. [ link | arXiv | pdf ]
  30. André. Schlichting. Time discretisation for a class of singular phase field models. Adv. Math. Sci. Appl. 55 (2009) 665–700. [ link | pdf ]

Proceedings

  1. Chun Yin Lam, André Schlichting. Thermodynamic limit of stochastic particle systems via EDP convergence. Oberwolfach Report 57/2023. [ link | pdf ]
  2. Antonio Esposito, Georg Heinze, Jan-Frederik Pietschmann, André Schlichting. Graph-to-local limit for a multi-species nonlocal cross-interaction system. Proceedings in Applied Mathematics & Mechanics, 2023. [ doi | arXiv | pdf ]
  3. José A. Carrillo, Rishabh Gvalani, Grigorios A. Pavliotis, André Schlichting, Christian Seis. Phase transitions and a mountain pass theorem in the space of probability measures, Oberwolfach Report  10/2021.  [ link | pdf ]
  4. Antonio Esposito, Francesco Patacchini, Dejan Slepčev, André Schlichting, Christian Seis. Nonlocal equations on discrete spaces inspired by numerical schemes, Oberwolfach Report 29/2020. [ link | pdf ]
  5. Joseph G. Conlon, André Schlichting. A non-local Fokker-Planck equation related to nucleation and coarsening, Oberwolfach Report 6/2018. [ link | pdf ]
  6. A. Schlichting, M. Slowik. Capacitary inequalities in discrete setting and application to metastable Markov chains, Oberwolfach Report 35/2015. [ link | pdf ]
  7. E. Boissard, N. Gozlan, J. Lehec, C. Léonard, G. Menz, A. Schlichting.
    Some recent developments in functional inequalities. Journées MAS 2012. ESAIM: Proc. 44 338-354 (2014) [ link | pdf ]
  8. A. Schlichting and W. Sproessig. Norm estimations of the modified Teodorescu transform with application to a multidimensional equation of airy type.
    AIP Conference Proceedings, 1048(1):701-705, September 2008. [ doi | pdf ]

Thesis

  1. André Schlichting. Phase Transitions in Interacting Systems, Universität Bonn, Habilitation thesis, 2020. [ pdf ]
  2. André Schlichting. The Eyring-Kramers formula for Poincaré and logarithmic Sobolev inequalities, Universität Leipzig, PhD thesis, 2012. [ Qucosa | pdf ]
  3. A. Schlichting. Solvability, approximation and estimates for a class of singular
    phase field models. Master’s thesis, University of Mining and Technology Freiberg and University of Pavia, Diploma thesis, 2008. [ pdf ]