Teaching
People
Teaching
Research
My main field of interest is probability theory. This includes large deviations, Brownian motion,
stochastic process in random media, random networks and applications of probability in analysis
and outside mathematics. I also have an interest in geometric measure theory, in particular
in connection with probability.
I am serving on the editorial board of
Journal of Theoretical 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 2327th 2009, organised jointly with
Julien Berestycki.

British Probability Meeting
"New random geometries and other recent developments in probability", Bath, September 711th 2009.

BathBerlin 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 1014th 2014,
organised jointly with Michiel Renger and Max von Renesse.
Here is a list of my
coauthors with links if available.
Nathanaël Berestycki,
Jochen Blath,
Valentina Cammarota,
Xia Chen,
Andrea Collevecchio,
Donald Dawson,
Amir Dembo,
Steffen Dereich,
Kwabena DokuAmponsah,
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,
Hubert Lacoin,
Günter Last,
Christian Mönch,
Marcel Ortgiese,
Yuval Peres,
David Preiss,
István Redl,
Scott Sheffield,
NarnRueih Shieh,
Nadia Sidorova,
Hermann Thorisson,
Pascal Vogt,
Vitali Wachtel,
Johannes Zimmer.
Here you find a list of my publications.
Books
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) 313324.

Symmetry properties of average densities and tangent measure distributions
of measures on the line,
Advances in Applied Mathematics 21, (1998) 146179.

Tangent measure distributions of hyperbolic Cantor sets,
with Daniela Krieg,
Monatshefte für Mathematik 126, (1998) 313328.

Tangent measure distributions of fractal measures,
with David Preiss,
Mathematische Annalen 312, (1998) 5393.

The average density of the path of planar Brownian motion
Stochastic Processes and their Applications 74, (1998) 133149.

Average densites, tangent measures and rectifiability
Periodica Mathematica Hungarica 37, (1998) 6579.

Small scale limit theorems for the intersection local times of
Brownian motion
with NarnRueih Shieh,
Electronic Journal of Probability 4, (1999) Paper 9, 123.

A set with finite curvature and projections of zero length,
with Helen Joyce,
Journal of Math. Analysis and Applications 247, (2000) 126135.

Almost sure Kallianpur Robbins laws for Brownian motion
in the plane,
Probability Theory and Related Fields, 118, (2000) 4964.

The average density of superBrownian motion
Annales de l'Institut Henri Poincare: Probab. et Stat.
37, (2001) 71100.

How fast are the particles of superBrownian motion?
Probability Theory and Related Fields, 121, (2001) 171197.

Thin and thick points for branching measure on a GaltonWatson tree
with NarnRueih Shieh.
Statistics and Probability Letters, 58, (2002) 1322.

Brownian intersection local times: Upper tail asymptotics
and thick points
with Wolfgang König,
Annals of Probability, 30, (2002) 16051656.

Strong clumping of superBrownian motion in a stable
catalytic medium
with Donald A. Dawson and Klaus Fleischmann,
Annals of Probability, 30, (2002) 19902045.

On the multifractal spectrum for branching measure on a GaltonWatson tree
with NarnRueih Shieh.
Journal of Applied Probability 41, (2004) 12231229.

Thick points of superBrownian motion
with Jochen Blath.
Probability Theory and Related Fields. 131, (2005) 604630.

A construction of catalytic superBrownian motion via collision local time
with Pascal Vogt.
Stochastic Processes and their Applications. 115, (2005) 7790.

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) 971996.

The multifractal spectrum of Brownian intersection local times
with Achim Klenke. Annals of Probability 33, (2005) 12551301.

Brownian intersection local times: Exponential moments and law of
large masses
with Wolfgang König.
Transactions of the American Mathematical Society 358, (2006) 12231255.

Hydrodynamic limit fluctuations of superBrownian motion with a stable catalyst
with Klaus Fleischmann and Vitali Wachtel.
Electronic Journal of Probability 11, (2006) 723767.

The universality classes in the parabolic Anderson model
with Remco van der Hofstad and Wolfgang König.
Communications in Mathematical Physics 267, (2006) 307353.

Small value probabilities via the branching tree heuristic.
with Marcel Ortgiese.
Bernoulli 14, (2008) 277299.

Moderate deviations for
random walk in random scenery
with Klaus Fleischmann and Vitali Wachtel.
Stochastic Processes and their Applications 118, (2008) 17681802.

A class of weakly selfavoiding walks
with Nadia Sidorova.
Journal of Statistical Physics 133, (2008) 255269.

Weak and almost sure limits for the parabolic Anderson model with heavytailed potentials
with Remco van der Hofstad and Nadia Sidorova.
Annals of Applied Probability 18, (2008) 24502494.

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 NarnRueih Shieh.
Probability Theory and Related Fields 143 (2009) 113136.

Upper tails for intersection local times of random walks in supercritial dimensions
with Xia Chen.
Journal of the London Mathematical Society, 79 (2009) 186210.

A two cities theorem for the parabolic Anderson model
with Wolfgang König, Hubert Lacoin and Nadia Sidorova.
Annals of Probability, 37 (2009) 347392.

Random networks with sublinear preferential attachment: Degree evolutions
with Steffen Dereich.
Electronic Journal of Probability, 14 (2009) 12221267.

Multiple intersection exponents for planar Brownian motion
with Achim Klenke.
Journal of Statistical Physics, 136 (2009) 373397.

Simultaneous multifractal analysis of branching and visibility measure on a
GaltonWatson tree
with Adam Kinnison.
Advances in Applied Probability, 42 (2010) 226245.

The Hausdorff dimension of the double points on the Brownian frontier
with Richard Kiefer.
Journal of Theoretical Probability, 23 (2010) 605623.

Phase transitions for dilute particle systems with LennardJones potential
with Andrea Collevecchio, Wolfgang König, and Nadia Sidorova.
Communications in Mathematical Physics, 299 (2010) 603630.

Large deviation principles for empirical measures of coloured random graphs
with Kwabena DokuAmponsah.
Annals of Applied Probability, 20 (2010) 19892021. Erratum.

Trap models with vanishing drift: Scaling limits and ageing regimes
with Nina Gantert and Vitali Wachtel.
ALEA, 7 (2010) 477501.

Random networks with concave preferential attachment rule.
with Steffen Dereich.
Jahresberichte der Deutschen Mathematiker Vereinigung 113 (2011) 2140.

Ageing in the parabolic Anderson model
with Marcel Ortgiese and Nadia Sidorova.
Annales de l'Institut Henri Poincare: Probab. et Stat. 47 (2011) 9691000.
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, 19.

Typical distances in ultrasmall random networks
with Steffen Dereich and Christian Mönch.
Advances in Applied Probability. 44 (2012) 583601.

Random networks with sublinear preferential attachment: the giant component
with Steffen Dereich.
Annals of Probability. 41 (2013) 329384.

Emergence of condensation in Kingman's model of selection and mutation
with Steffen Dereich.
Acta Applicandae Mathematicae. 127 (2013) 1726.

Unbiased shifts of Brownian motion
with Günter Last and Hermann Thorisson.
Annals of Probability. 42 (2014) 431463.

GaltonWatson trees with vanishing martingale limit
with Nathanaël Berestycki, Nina Gantert and Nadia Sidorova.
Journal of Statistical Physics. 155 (2014) 737762.

Vulnerability of robust preferential attachment networks
with Maren Eckhoff.
Electronic Journal of Probability. 19 (2014) Paper 57, 147.

Spatial preferential attachment networks: Power laws and clustering coefficients
with Emmanuel Jacob.
Annals of Applied Probability. 25 (2015) 632662.

Cycle length distributions in random permutations with diverging cycle weights
with Steffen Dereich.
Random Structures and Algorithms. 46 (2015) 635650.
Papers published in books

On onesided 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 427436.
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. 135150. Birkhäuser Verlag (2004).

Multifractal analysis of branching measure on a GaltonWatson tree
with NarnRueih 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. 655662. 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. 99120. Cambridge University Press (2009).

Random fractals
Contributed chapter to New Perspectives in Stochastic Geometry.
Edited by W. Kendall and I. Molchanov.
pp.275304. Oxford University Press (2010).

The parabolic Anderson model with heavytailed 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.6785. 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.247271. 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 1425. Springer Lecture Notes in Computer Science, Vol. 8305 (2013).
Papers submitted for publication
Theses

"Ergodische Zerlegungen invarianter BaireMaße",
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
Technical reports, unpulished papers and extended abstracts

Selfsimilar random measures and tangent measure distributions,
Extended abstract. 5th Workshop on Probability Theory and its Applications, Bielefeld,
Germany, Februar 1999.

Pathwise KallianpurRobbins laws for Brownian motion in the plane.
Preprint 319. Fachbereich Mathematik, Universität Kaiserslautern.
The director's cut of Almost sure KallianpurRobbins 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 KPPGleichung,
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 nonclassical random processes. Oberwolfach (2005).

Complete localisation in the parabolic Anderson model with Paretodistributed 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'autointersections'. Luminy (2010).
Actes des rencontres du CIRM 2 (2010) 2729.

A conditioning principle for GaltonWatson trees
Unpublished manuscript, with Nathanaël Berestycki and Nadia Sidorova.
Book reviews
Slides of selected talks
This page contains Free Gifs and Animations
Last updated by Peter Mörters on August 5th 2013.
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