Michiel Renger

Research interests

• Reacting particle systems and other jump processes on discrete spaces
• Non-equilibrium thermodynamics, macroscopic fluctuation theory
• PDE's, variational calculus and gradient flows

Teaching

In the summer 2020 I taught a course in large deviations at the TU Berlin.

In the summer 2018 I taught a course in convex analysis at the TU Berlin. Click for the (handwritten) lecture notes with exercises.

Publications

Preprints

• R.I.A. Patterson, D.R.M. Renger and U. Sharma, Variational structures beyond gradient flows: a macroscopic fluctuation-theory perspective. ArXiv Preprint 2103.14384 (2021).
• N. Nüsken and D.R.M. Renger, Stein Variational Gradient Descent: many-particle and long-time asymptotics. ArXiv Preprint 2102.12956 (2021).
• A. Agazzi, L. Andreis, R.I. A. Patterson and D.R.M. Renger, Large deviations for Markov jump processes with uniformly diminishing rates ArXiv Preprint 2102.13040 (2021).
• M.A. Peletier and D.R.M. Renger, Fast reaction limits via Γ-convergence of the Flux Rate Functional. ArXiv Preprint 2009.14546 (2020).

Peer-reviewed publications

• D. Gabrielli and D.R.M. Renger, Dynamical Phase Transitions for Flows on Finite Graphs. Journal of Statistical Physics 181, 2353-2371 (2020).
• D.R.M. Renger and J. Zimmer, Orthogonality of fluxes in general nonlinear reaction networks. Discrete & Continuous Dynamical Systems - S 14 (1), 205-217 (2021).
• R.I.A. Patterson and D.R.M. Renger, Large Deviations of Jump Process Fluxes (view-only version). Mathematical Physics, Analysis and Geometry First Online (2019).
• M. Heida, R.I.A. Patterson and D.R.M. Renger, Topologies and measures on the space of functions of bounded variation taking values in a Banach or metric space (view-only version). Journal of Evolution Equations 19, 1 (2019).
• D.R.M. Renger, Gradient and GENERIC systems in the space of fluxes, applied to reacting particle systems. Entropy, special issue "Probability Distributions and Maximum Entropy in Stochastic Chemical Reaction Networks" 20, 8 (2018). See also: D.R.M. Renger, Generalised Gradient Systems and GENERIC in Flux Space. Oberwolfach Report 1746 (2018).
• D.R.M. Renger, Flux large deviations of independent and reacting particle systems, with implications for Macroscopic Fluctuation Theory. Journal of Statistical Physics 172, 5 (2018).
• P. Koltai and D.R.M. Renger, From large deviations to semidistances of transport and mixing: coherence analysis for finite Lagrangian data. Journal of Nonlinear Science 28, 5 (2018).
• A. Mielke, R.I.A. Patterson, M.A. Peletier and D.R.M. Renger, Non-equilibrium thermodynamical principles for chemical reactions with mass-action kinetics. SIAM Journal on Applied Mathematics 77, 4 (2017).
• M. Liero, A. Mielke, M.A. Peletier and D.R.M. Renger, On microscopic origins of generalized gradient structures. Discrete and Continuous Dynamical Systems - Series S 10, 1 (2017).
• A. Mielke, M. A. Peletier, and D.R.M. Renger, A generalization of Onsager's reciprocity relations to gradient flows with nonlinear mobility. Journal of Non-Equilibrium Thermodynamics 41, 2 (2016).
• M. Erbar, J. Maas and D.R.M. Renger, From large deviations to Wasserstein gradient flows in multiple dimensions. Electronic Communications in Probability 20, 89 (2015).
• A. Mielke, M. A. Peletier, D.R.M. Renger, On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion. Potential Analysis 41, 4 (2014).
• M. Duong, V. Laschos and M. Renger, Wasserstein gradient flows from large deviations of many-particle limits. ESAIM: Control, Optimisation and Calculus of Variations 19, 4 (2013).
• M.A. Peletier, D.R.M. Renger and M. Veneroni, Variational formulation of the Fokker-Planck equation with decay: a particle approach. Communications in Contemporary Mathematics 15, 5 (2013).

Proceedings

• J.H.M. Evers, D. Kiss, W. Kowalczyk, T. Navilarekallu, M. Renger, L. Sella, V. Timperio, A. Viorel, A.C.C. van Wijk and A.N. Yzelman, Node counting in wireless ad-hoc networks. Proceedings of the 79th European Study Group Mathematics with Industry, Amsterdam, the Netherlands (2012).

PhD thesis

• D.R.M. Renger. Microscopic interpretation of Wasserstein gradient flows. Technische Universiteit Eindhoven (2013).

Publications (collaboration engineering)

In 2008, I researched topics in "collaboration engineering" at the Technology, Policy and Management Department of the TU Delft. Click here to show/hide these publications. >

Popular Science

• 11 Mai 2019: "Schallwellen in elektronischer Musik", Tag der Mathematik at Beuth Hochschule, Berlin, Germany.
• 28 July 2017: "Was sind und was sollen die Zahlen?", Tag der Mathematik at Universität Regensburg, Regensburg, Germany.
• 22 April 2017: "Wie man nicht-differenzierbare Funktionen differenzieren kann", Tag der Mathematik at Humboldt-Universität, Berlin, Germany.
• 15 April 2016: "The truth is out there... it's called math!", Nerd Nite Greatest Hits - Five years of Talks and Beers at Felix Meritis, Amsterdam, the Netherlands.
• 9 May 2015: "Minimierung in unendlich vielen Dimensionen", Tag der Mathematik at Beuth Hochschule, Berlin, Germany.
• 6 June 2014: Here is my talk "Infinity: imagining the unimaginable", Nerd Nite XVII at Crea Muziekzaal, Amsterdam, the Netherlands:

• 17 May 2014: "Die Entropie von unendlich vielen Molekülen", Tag der Mathematik at Technische Universität, Berlin, Germany.
• 10 May 2014: "Unendlichtkeit", 14. Lange Nacht der Wissenschaften at Geschäftsstelle der Leibniz-Gemeinschaft, Berlin, Germany.