Peter Mörters Professor of Probability Head of Statistics Department of Mathematical Sciences University of Bath Claverton Down Bath BA2 7AY United Kingdom Telephone +44-1225-386216 e-mail: maspm@bath.ac.uk Contents Research

Academic Service.

Publications.

Teaching

Lecture Notes.

Graduate Courses.

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 courses

• I was speaking on Random networks: the preferential attachment paradigm
  at the LMS-EPSRC Short Course "Topics in Probability" organised by Alison Etheridge from April 3rd - 8th 2011 in Oxford. For details see here.
• I was speaking on Sample path properties of Brownian motion
  at the BMS Summer School, September 26th to October 7th 2011 in Berlin. For details see here.
• In Semester I of 1011/12 I will teach a graduate course on Brownian motion as part of the Mathematics Taught Course Centre.
  A link to the course webpage is here.

Research

Academic Service

I am serving on the editorial board of Electronic Journal of Probability and Electronic Communications in Probability.

I was involved in the organisation of the following recent conferences:

• 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"
  in Bath, September 7-11th 2009.

• Bath-Berlin Workshop "Phase boundaries and random polymers"
  Organisers Nicolas Dirr, Peter Mörters and Max von Renesse.
  Bath 12.9.-14.9.2011

• "Minisymposium on random measures" in Bath 21.9.2011

• Oberwolfach Conference "Interplay of Analysis and Probability in Physics"
  Organisers Wolfgang König, Peter Mörters, Mark Peletier and Johannes Zimmer.
  Oberwolfach, Germany 22.1.- 28.1.2012

Mathematical Publications:

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

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 in journals

• Average densities and linear rectifiability of measures,
  Mathematika 44, (1997) 313-324.
• Symmetry properties of average densities and tangent measure distributions of measures on the line,
  Advances in Applied Mathematics 21, (1998) 146-179.
• Tangent measure distributions of hyperbolic Cantor sets,
  with Daniela Krieg, Monatshefte für Mathematik 126, (1998) 313-328.
• Tangent measure distributions of fractal measures,
  with David Preiss, Mathematische Annalen 312, (1998) 53-93.
• The average density of the path of planar Brownian motion
  Stochastic Processes and their Applications 74, (1998) 133-149.
• Average densites, tangent measures and rectifiability
  Periodica Mathematica Hungarica 37, (1998) 65-79.
• Small scale limit theorems for the intersection local times of Brownian motion
  with Narn-Rueih Shieh, Electronic Journal of Probability 4, (1999) Paper 9, 1-23.
• A set with finite curvature and projections of zero length,
  with Helen Joyce, Journal of Math. Analysis and Applications 247, (2000) 126-135.
• Almost sure Kallianpur Robbins laws for Brownian motion in the plane,
  Probability Theory and Related Fields, 118, (2000) 49-64.
• The average density of super-Brownian motion
  Annales de l'Institut Henri Poincare: Probab. et Stat. 37, (2001) 71-100.
• How fast are the particles of super-Brownian motion?
  Probability Theory and Related Fields, 121, (2001) 171-197.
• Thin and thick points for branching measure on a Galton-Watson tree
  with Narn-Rueih Shieh. Statistics and Probability Letters, 58, (2002) 13-22.
• Brownian intersection local times: Upper tail asymptotics and thick points
  with Wolfgang König, Annals of Probability, 30, (2002) 1605-1656.
• Strong clumping of super-Brownian motion in a stable catalytic medium
  with Donald A. Dawson and Klaus Fleischmann, Annals of Probability, 30, (2002) 1990-2045.
• On the multifractal spectrum for branching measure on a Galton-Watson tree
  with Narn-Rueih Shieh. Journal of Applied Probability 41, (2004) 1223-1229.
• Thick points of super-Brownian motion
  with Jochen Blath. Probability Theory and Related Fields. 131, (2005) 604-630.
• A construction of catalytic super-Brownian motion via collision local time
  with Pascal Vogt. Stochastic Processes and their Applications. 115, (2005) 77-90.
• Large deviations of Markov chains indexed by random trees
  with Amir Dembo and Scott Sheffield. Annales de l'Institut Henri Poincare: Probab. et Stat. 41, (2005) 971-996.
• The multifractal spectrum of Brownian intersection local times
  with Achim Klenke. Annals of Probability 33, (2005) 1255-1301.
• Brownian intersection local times: Exponential moments and law of large masses
  with Wolfgang König. Transactions of the American Mathematical Society 358, (2006) 1223-1255.
• Hydrodynamic limit fluctuations of super-Brownian motion with a stable catalyst
  with Klaus Fleischmann and Vitali Wachtel. Electronic Journal of Probability 11, (2006) 723-767.
• The universality classes in the parabolic Anderson model
  with Remco van der Hofstad and Wolfgang König. Communications in Mathematical Physics 267, (2006) 307-353.
• Small value probabilities via the branching tree heuristic.
  with Marcel Ortgiese. Bernoulli 14, (2008) 277–299.
• Moderate deviations for random walk in random scenery
  with Klaus Fleischmann and Vitali Wachtel. Stochastic Processes and their Applications 118, (2008) 1768-1802.
• A class of weakly self-avoiding walks
  with Nadia Sidorova. Journal of Statistical Physics 133, (2008) 255–269.
• Weak and almost sure limits for the parabolic Anderson model with heavy-tailed potentials
  with Remco van der Hofstad and Nadia Sidorova. Annals of Applied Probability 18, (2008) 2450–2494.
• Minimal supporting subtrees for the free energy of polymers on disordered trees
  with Marcel Ortgiese. Journal of Mathematical Physics 49 (2008) 21 pages.
• The exact packing measure of Brownian double points
  with Narn-Rueih Shieh. Probability Theory and Related Fields 143 (2009) 113-136.
• Upper tails for intersection local times of random walks in supercritial dimensions
  with Xia Chen. Journal of the London Mathematical Society, 79 (2009) 186-210.
• A two cities theorem for the parabolic Anderson model
  with Wolfgang König, Hubert Lacoin and Nadia Sidorova. Annals of Probability, 37 (2009) 347–392.
• Random networks with sublinear preferential attachment: Degree evolutions
  with Steffen Dereich. Electronic Journal of Probability, 14 (2009) 1222-1267.
• Multiple intersection exponents for planar Brownian motion
  with Achim Klenke. Journal of Statistical Physics, 136 (2009) 373-397.
• Simultaneous multifractal analysis of branching and visibility measure on a Galton-Watson tree
  with Adam Kinnison. Advances in Applied Probability, 42 (2010) 226-245.
• The Hausdorff dimension of the double points on the Brownian frontier
  with Richard Kiefer. Journal of Theoretical Probability, 23 (2010) 605-623.
• Phase transitions for dilute particle systems with Lennard-Jones potential
  with Andrea Collevecchio, Wolfgang König, and Nadia Sidorova. Communications in Mathematical Physics, 299 (2010) 603-630.
• Large deviation principles for empirical measures of coloured random graphs
  with Kwabena Doku-Amponsah. Annals of Applied Probability, 20 (2010) 1989–2021.
• Trap models with vanishing drift: Scaling limits and ageing regimes
  with Nina Gantert and Vitali Wachtel. ALEA, 7 (2010) 477-501.
• 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.
  

Papers published in books

• On one-sided average densities of fractal measures on the line with David Preiss.
  In: Seminaire Initiation a l'analyse, 34eme annee 1994/1995, Artikel No.4.
  Publ. Univ. Pierre et Marie Curie (1995).
• A pathwise version of Spitzer's Law
  In Limit theorems in Probability and Statistics, Vol. II,
  Proceedings of the 4th Hungarian Colloquium held in honour of the 65th birthday of Pal Revesz in Balatonlelle, 1999.
  Edited by I. Berkes, E. Csaki and M. Csörgö, pp 427--436. Janos Bolyai Math. Soc., Budapest (2002).
• Intersection exponents and the multifractal spectrum for measures on Brownian paths
  In Fractal Geometry and Stochastics III,
  Edited by C. Bandt, U. Mosco and M. Zähle. Progress in Probability, Vol. 57, pp. 135-150. Birkhäuser Verlag (2004).
• Multifractal analysis of branching measure on a Galton-Watson tree with Narn-Rueih Shieh.
  In Proceedings of the 3rd International Conference of Chinese Mathematicians, Hong Kong, 2004.
  Edited by K.-S. Lau, Z.-P. Xin and S.-T. Yau, pp. 655-662. International Press/AMS (2008).
  
• Why study multifractal spectra?
  In Trends in Stochastic Analysis: A Festschrift in Honour of Heinrich v. Weizsäcker.
  Edited by J. Blath, P. Mörters and M. Scheutzow. pp. 99-120. Cambridge University Press (2009).
  
• Random fractals
  Contributed chapter to New Perspectives in Stochastic Geometry.
  Edited by W. Kendall and I. Molchanov. pp.275-304. Oxford University Press (2010).
  
• 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).

Papers in press

• Emergence of condensation in Kingman's model of selection and mutation
  with Steffen Dereich. To appear in Acta Applicandae Mathematicae.
  
• Unbiased shifts of Brownian motion
  with Günter Last and Hermann Thorisson. To appear in Annals of Probability.
  

Submitted papers

• Galton-Watson trees with vanishing martingale limit
  with Nathanaël Berestycki, Nina Gantert and Nadia Sidorova.
• Spatial preferential attachment networks: Power laws and clustering coefficients
  with Emmanuel Jacob.
• Cycle length distributions in random permutations with diverging cycle weights
  with Steffen Dereich.

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 'Déviations 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.