Prof. Dr. Peter Mörters

Research

My main field of interest is probability theory. This includes random graphs and networks, large deviations, Brownian motion, stochastic processes in random media, and applications of probability in analysis and outside mathematics. I also have an interest in geometric measure theory, in particular in connection with probability.

Coauthors

Here is a list of my coauthors with links if available.

Nathanaël Berestycki, Volker Betz, Jakob Björnberg, Jochen Blath, Valentina Cammarota, Xia Chen, Andrea Collevecchio, Donald Dawson, Amir Dembo, Steffen Dereich, Kwabena Doku-Amponsah, Maren Eckhoff, John Fernley, Klaus Fleischmann, Nina Gantert, Horacio González Duhart , Peter Gracar , Arne Grauer , Markus Heydenreich , Remco van der Hofstad, Pim van der Hoorn, Emmanuel Jacob, Helen Joyce, Céline Kerriou, Richard Kiefer, Adam Kinnison, Achim Klenke, Wolfgang König , Simon Korbel, Marilyn Korfhage, Daniela Krieg, Joachim Krug, Andreas Kyprianou, Hubert Lacoin, Francis Lane, Günter Last, Amitai Linker, Lukas Lüchtrath , Cécile Mailler, Neeladri Maitra, Sam Moore, Christian Mönch, Marcel Ortgiese, Su-Chan Park, Yuval Peres, David Preiss, István Redl, Tim Rogers, Lucas Schätze, Nick Schleicher, Anna Senkevich, Scott Sheffield, Narn-Rueih Shieh, Nadia Sidorova, Christian Sohler, Léo Touzo, Hermann Thorisson, Daniel Ueltschi, Pascal Vogt, Vitali Wachtel, Stefan Walzer, Johannes Zimmer.

Papers published or accepted in journals (2021-)

• Percolation phase transition in weight-dependent random connection models
  with Peter Gracar and Lukas Lüchtrath. Advances in Applied Probability 53 (2021), 1090–1114 .
• Competing growth processes with random growth rates and random birth times
  with Cécile Mailler and Anna Senkevich. Stochastic Processes and their Applications 135 (2021), 183-226.
• A path formula for the sock sorting problem
  with Simon Korbel. Theory of Probability and its Applications (Teor. Veroyatnost. i Primenen.) 26 (2021), 889-894 .
• Recurrence versus transience for weight-dependent random connection models
  with Peter Gracar, Markus Heydenreich and Christian Mönch. Electronic Journal of Probability 27 (2022), 889-894, Paper no. 60, 1-31.
• Chemical distance in geometric random graphs with long edges and scale-free degree distribution
  with Peter Gracar and Arne Grauer. Communications in Mathematical Physics 395 (2022), 859-906.
• Tangent graphs. Pure and Applied Functional Analysis 8 (2023) 1767-1779.
  
• Branching with selection and mutation I: Mutant fitness of Fréchet type
  with Su-Chan Park, Joachim Krug and Léo Touzo. Journal of Statistical Physics 190 (2023) 115.
• The contact process on dynamical scale-free networks
  with Emmanuel Jacob and Amitai Linker. Annales Institut H. Poincaré: Probab. et Stat. (to appear).
• The fewest-big-jumps principle and an application to random graphs
  with Céline Kerriou. Bernoulli Journal (to appear).
• A two-table theorem for a disordered Chinese restaurant process
  with Jakob E. Björnberg, Cécile Mailler and Daniel Ueltschi. Annals of Applied Probability (to appear).
• The contact process on a graph adapting to the infection
  with John Fernley and Marcel Ortgiese. Stochastic Processes and their Applications (to appear).

Papers presented at conferences and in books (2021-)

• The disordered Chinese restaurant and other competing growth processes
  with Cécile Mailler and Anna Senkevich.
  31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020) ,
  LIPIcs 159, 21:1-21:13, 2020.
• A sublinear local access implementation for the Chinese restaurant process
  with Christian Sohler and Stefan Walzer.
  Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022),
  LIPIcs 245, 28:1–28:18, 2022.
• Early typical vertices in subcritical random graphs of preferential attachment type
  with Nick Schleicher.
  35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024) ,
  LIPIcs 302, 14:1-14:10, 2024.

Papers submitted for publication

• Robustness in the Poisson Boolean model with convex grains
  with Peter Gracar and Marilyn Korfhage.
• Metastability of the contact process on slowly evolving scale-free networks
  with Emmanuel Jacob and Amitai Linker.
• Condensation in scale-free geometric graphs with excess edges
  with Pim van der Hoorn, Remco van der Hofstad, Céline Kerriou and Neeladri Maitra.
• The size of the giant in inhomogeneous random graphs of preferential attachment type
  with Lucas Schätze.
• Branching with selection and mutation II: Mutant fitness of Gumbel type
  with Su-Chan Park and Joachim Krug.
• The largest subcritical component in inhomogeneous random graphs of preferential attachment type
  with Nick Schleicher.

Papers published up to 2011-2020 [31]

Papers published 2001-2010 [33]

Papers published up to 2000 [10]

Theses

• Ergodische Zerlegungen invarianter Baire-Maße,
  Diplomarbeit, Universität Kaiserslautern, (1991).
• Tangent Measure Distributions and the Geometry of Measures,
  PhD thesis, University of London, (1995).
• Contributions to Fractal Geometry and Stochastic Processes,
  Habilitation thesis, Universität Kaiserslautern, (2001).

Popular maths

• Backgammon, doubling the stakes, and Brownian motion
  with Jochen Blath. Plus, 15, 2001.

Technical reports, unpublished papers and extended abstracts

• Self-similar random measures and tangent measure distributions,
  Extended abstract. 5th Workshop on Probability Theory and its Applications, Bielefeld, Germany, Februar 1999.
• Pathwise Kallianpur-Robbins laws for Brownian motion in the plane.
  Preprint 319. Fachbereich Mathematik, Universität Kaiserslautern.
  The director's cut of Almost sure Kallianpur-Robbins laws with many spectacular extras.
• A uniform dimension result for the Brownian snake
  Preprint Nummer 478 in the Preprint series of WIAS Berlin.
• Eine wahrscheinlichkeitstheoretische Untersuchung der KPP-Gleichung,
  Wissenschaftlicher Vortrag im Rahmen des Habilitationsverfahrens, November 2001.
• Benfords Gesetz über die Verteilung der Ziffern,
  Habilitationsvorlesung, November 2001.
• Intersection local time of Brownian motion: Tail behaviour and fractal applications.
  Extended abstract. 4th Symposium on Levy processes: Theory and applications. Manchester (2005).
  
• The universality classes in the parabolic Anderson model.
  Extended abstract. Workshop on stochastic analysis and non-classical random processes. Oberwolfach (2005).
  
• Complete localisation in the parabolic Anderson model with Pareto-distributed potential,
  Unpublished manuscript, with Wolfgang König and Nadia Sidorova (2006).
• A class of random measures and their fractal geometry.
  Extended abstract. Workshop on perspectives in stochastic geometry. Oberwolfach (2008).
  
• Upper tail asymptotics for the intersection local times of random walks in high dimensions.
  Extended abstract. Workshop 'Deviations pour les temps locaux d'auto-intersections'. Luminy (2010).
  Actes des rencontres du CIRM 2 (2010) 27-29.
• A conditioning principle for Galton-Watson trees
  Unpublished manuscript, with Nathanaël Berestycki and Nadia Sidorova.

Book reviews

• Perplexing Problems in Probability.
  Volume in Honor of Harry Kesten, edited by M. Bramson and R. Durrett.
  Birkhäuser Verlag.
  Statistics and Decisions 19/2 (2001) 218-220.
• High Dimensional Probability II.
  Proceedings of the 2nd conference on High dimensional Probability, Washington 1999,
  edited by E. Gine, D.M. Mason and J.A. Wellner. Birkhäuser Verlag.
  Statistics and Decisions 20/3 (2002) 323-325.
• Random walk intersections: Large deviations and related topics.
  by Xia Chen. AMS Mathematical Surveys and Monographs Volume 157.
  Bulletin of the London Mathematical Society 43 (2011) 823-825.

Slides of selected talks

• The parabolic Anderson model with heavy-tailed potential
  Plenary Talk at 33rd Conference on Stochastic Processes and their Applications, Berlin, July 2009.
• Tossing coins, matching points and shifting Brownian motion
  Colloquium Talk at BMS Fridays, Berlin, July 2012.
• Condensation in models of selection and mutation
  Random Combinatorial Structures and Statistical Mechanics, Venice, May 2013.
• Robustness of spatial preferential attachment networks
  Random walks on graphs and potential theory, Warwick, May 2015.

Academic Service

I am serving on the editorial board of Journal of Theoretical Probability.
I am serving on the editorial board of Stochastic Processes and Applications.

Old Lecture Notes