Peter Mörters I have moved to the University of Cologne. This page is no longer updated, see here for my updated webpage. Visting Professor of Probability Department of Mathematical Sciences University of Bath Claverton Down Bath BA2 7AY United Kingdom Telephone +44-1225-386216 e-mail: maspm(at)bath.ac.uk Contents Research

Condensation project.

Academic Service.

Publications.

Teaching

Lecture Notes.

People

Current and former PhD students

Probability Lab at Bath.

Teaching

Lecture Notes

• Lecture Notes on Fractal Geometry.

• Lecture Notes on Probability Theory.

• Lecture Notes on Stochastic Analysis.

• Lecture Notes on Martingale Theory.

• Graduate Course Notes Hausdorff dimension, random trees and Brownian motion.

• Graduate Course Notes Sample path properties of Brownian motion.

• Graduate Course Notes Large deviation theory.

• Graduate Course Notes Brownian motion.

Research

Academic Service

I am organsing the following conference:

• Prob-L@B Workshop "Condensation phenomena in stochastic systems" Bath 4.7.-6.7.2016, organsied jointly with Stefan Grosskinsky and Cecile Mailler.

• LMS Southwest Regional Meeting and Workshop "Analysis and stochastics of growth processes" Bath 11.9.-15.9.2006

• International Conference "Modern perspectives in real and stochastic analysis" Kaiserslautern 2.4.-5.4.2007

• Section on Stochastic Processes in the 8th German Open Conference on Probability and Statistics, Aachen, 4.3.-7.3.2008.

• Conference Fractal Geometry and Stochastics IV Greifswald, 8.9.-12.9.2008.

• "Interplay of Analysis and Probability in Physics" Oberwolfach Workshop 30th November to 6th December 2008.

• YEP Workshop for Young European Probabilists. Series at Eurandom (Eindhoven, Netherlands).
  Workshop VI on Fragmentation and coagulation took place March 23-27th 2009, organised jointly with Julien Berestycki.

• British Probability Meeting "New random geometries and other recent developments in probability", Bath, September 7-11th 2009.

• Bath-Berlin Workshop "Phase boundaries and random polymers", Bath 12.9.-14.9.2011

• "Minisymposium on random measures" in Bath 21.9.2011

• "Interplay of Analysis and Probability in Physics" Oberwolfach Workshop, January 22nd to 28th 2012

• YEP Workshop for Young European Probabilists. Series at Eurandom (Eindhoven, Netherlands).
  Workshop XI on Mass transport in analysis and probability took place March 10-14th 2014,
  organised jointly with Michiel Renger and Max von Renesse.

• ICMS Workshop "Dynamical networks and network dynamics" Edinburgh 18.1.-22.1.2016, organised jointly with Tim Rogers.

• SAM Workshop "Variational Structures and Large Deviations for Interacting Particle Systems and Partial Differential Equations"
  Eurandom, Eindhoven 14.3-18.3.2016, organised jointly with Frank den Hollander and Mark Peletier.

Mathematical Publications:

Nathanaël Berestycki, Jochen Blath, Valentina Cammarota, Xia Chen, Andrea Collevecchio, Donald Dawson, Amir Dembo, Steffen Dereich, Kwabena Doku-Amponsah, Maren Eckhoff, Klaus Fleischmann, Nina Gantert, Horacio González Duhart , Remco van der Hofstad, Emmanuel Jacob, Helen Joyce, Richard Kiefer, Adam Kinnison, Achim Klenke, Wolfgang König, Daniela Krieg, Andreas Kyprianou, Hubert Lacoin, Francis Lane, Günter Last, Cécile Mailler, Christian Mönch, Marcel Ortgiese, Yuval Peres, David Preiss, István Redl, Scott Sheffield, Narn-Rueih Shieh, Nadia Sidorova, Hermann Thorisson, Daniel Ueltschi, Pascal Vogt, Vitali Wachtel, Johannes Zimmer.

Here you find a list of my publications.

Books

Brownian motion with Yuval Peres. Cambridge Series in Statistical and Probabilistic Mathematics, Volume 30. An errata page for this book is here.

Books edited

"Analysis and Stochastics of Growth Processes and Interface Models", Edited by Peter Mörters, Roger Moser, Hartmut Schwetlick, Mathew Penrose and Johannes Zimmer. Oxford University Press, 2008. "Trends in Stochastic Analysis: A Festschrift in Honour of Heinrich v. Weizsäcker", Edited by Jochen Blath, Peter Mörters and Michael Scheutzow. Cambridge University Press, 2009. "Fractal Geometry and Stochastics IV", Edited by Christoph Bandt, Peter Mörters and Martina Zähle. Birkhäuser, Progress in Probability Volume 61, 2009.

Papers published up to 2000 [10]

Papers published 2001-2010 [33]

Papers published in journals (2011-)

• Random networks with concave preferential attachment rule.
  with Steffen Dereich. Jahresberichte der Deutschen Mathematiker Vereinigung 113 (2011) 21-40.
• Ageing in the parabolic Anderson model
  with Marcel Ortgiese and Nadia Sidorova. Annales de l'Institut Henri Poincare: Probab. et Stat. 47 (2011) 969-1000.
  Supplement: Animation of limiting process.
• On the most visited sites of planar Brownian motion
  with Valentina Cammarota. Electronic Communications in Probability 17 (2012) Paper 15, 1-9.
• Typical distances in ultrasmall random networks
  with Steffen Dereich and Christian Mönch. Advances in Applied Probability. 44 (2012) 583-601.
  
• Random networks with sublinear preferential attachment: the giant component
  with Steffen Dereich. Annals of Probability. 41 (2013) 329-384.
  
• Emergence of condensation in Kingman's model of selection and mutation
  with Steffen Dereich. Acta Applicandae Mathematicae. 127 (2013) 17-26.
  
• Unbiased shifts of Brownian motion
  with Günter Last and Hermann Thorisson. Annals of Probability. 42 (2014) 431-463.
  
• Galton-Watson trees with vanishing martingale limit
  with Nathanaël Berestycki, Nina Gantert and Nadia Sidorova. Journal of Statistical Physics. 155 (2014) 737-762.
  
• Vulnerability of robust preferential attachment networks
  with Maren Eckhoff. Electronic Journal of Probability. 19 (2014) Paper 57, 1-47.
• Spatial preferential attachment networks: Power laws and clustering coefficients
  with Emmanuel Jacob. Annals of Applied Probability. 25 (2015) 632-662.
  
• Cycle length distributions in random permutations with diverging cycle weights
  with Steffen Dereich. Random Structures and Algorithms. 46 (2015) 635-650.
  
• Skorokhod embeddings for two-sided Markov chains
  with István Redl. Probability Theory and Related Fields 165 (2016) 483-508.
  
• Condensation and symmetry-breaking in the zero-range process with weak site disorder
  with Cécile Mailler and Daniel Ueltschi. Stochastic Processes and their Applications 126 (2016) 3283-3309.
• The largest fragment of a homogeneous fragmentation process
  with Andreas Kyprianou and Francis Lane. Journal of Statistical Physics 166 (2017) 1226-1246.
• Robustness of scale-free spatial networks
  with Emmanuel Jacob. Annals of Probability 45 (2017) 1680-1722.
• Optimal embeddings by unbiased shifts of Brownian motion
  with István Redl. Bulletin of the London Mathematical Society 49 (2017) 331-341.
• The contact process on scale-free networks evolving by vertex updating
  with Emmanuel Jacob. Royal Society Open Science, 4 (2017) Issue 5.

Papers published in books (2011-)

• The parabolic Anderson model with heavy-tailed potential.
  In Surveys in Stochastic Processes. Proceedings of the 33rd SPA Conference in Berlin, 2009.
  Edited by J. Blath, P. Imkeller, and S. Roelly. pp.67-85. EMS Series of Congress Reports (2011).
• A scaling limit theorem for the parabolic Anderson model with exponential potential with Hubert Lacoin.
  In Probability in complex physical systems. In Honour of Jürgen Gärtner and Erwin Bolthausen.
  Edited by J.-D. Deuschel, B Gentz, W König, M von Renesse, M Scheutzow, and U Schmock.
  pp.247--271. Springer Proceedings in Mathematics, Vol. 11 (2012).
• A spatial preferential attachment model with local clustering with Emmanuel Jacob.
  In Algorithms and Models for the Web Graph. Proceedings of the 10th International Workshop, WAW 2013, Cambridge, MA, USA.
  Edited by A. Bonato, M. Mitzenmacher, P. Pralat.
  pp 14--25. Springer Lecture Notes in Computer Science, Vol. 8305 (2013).
• Robustness of spatial preferential attachment networks with Emmanuel Jacob.
  In Algorithms and Models for the Web Graph. Proceedings of the 12th International Workshop, WAW 2015, Eindhoven, Netherlands.
  Edited by D. Gleich, J. Komjathy, N. Litvak.
  pp 3--14. Springer Lecture Notes in Computer Science, Vol. 9479 (2015).

Papers accepted for publication

• Non-extensive condensation in reinforced branching processes
  with Steffen Dereich and Cécile Mailler. To appear in Annals of Applied Probability.
  
• The semi-infinte asymmetric exclusion process: large deviations via matrix products
  with Horacio González Duhart and Johannes Zimmer. To appear in Potential Analysis.

Papers submitted for publication

• Distances in scale-free networks at criticality
  with Steffen Dereich and Christian Mönch.

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, unpulished 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.