Workshop on

"Hitting, returning and matching in dynamical systems,
information theory & mathematical biology"

November 3-7, 2008

EURANDOM, Eindhoven, The Netherlands

Programme | Abstracts| Speakers | Participants |Registration | Practical Information


The purpose of this workshop is to gather people from various areas dealing with probabilistic aspects of the occurrence and the repetition of events.

In the context of ergodic theory and dynamical systems, one deals with hitting and return times to “shrinking” sets, e.g., cylinder sets, balls, Bowen balls. The exponential rate of return to shrinking typical cylinders is the entropy of the system [5]. In hyperbolic systems, the return time to a typical ball scales as a power law, with exponent the Hausdorff dimension of the invariant measure. The smallest return time to ball is related to Lyapunov exponents [2]. Another subject is the search for limit laws of (rescaled) hitting and return times. For “chaotic" systems, this limiting law is exponential. The control of fluctuations relies on the control of the Poisson approximation [1].

The link between entropy and recurrence rate to cylinders was actually established in the context of information theory in the 1990’s, in relation with data compression; see [5]. In this field, one is interested in pattern matching, perfect or approximate (lossy data compression) [3]. In the theory of image compression, Gibbsian random fields naturally arise.

In mathematical biology, one analyses word occurrences in, e.g., DNA and protein sequences. A well-known algorithm for DNA matching, namely BLAST, relies on a Poisson approximation of the distribution of words. The validity and quality of this approximation is a current object of study.

People from the areas mentioned above deal with common objects (often under different names) with different motivations, applications and techniques. This meeting will be the opportunity to share expertises, ideas and sustain future projects and colloborations.

To summarise, we aim at covering the following subjects in the workshop:

·                 Entropy, hitting and return times in ergodic theory;

·                 Sequence alignment and occurrence of words in biological sequences;

·                 Occurrence and matching of patterns in stochastic processes and random fields;

·                 Pattern matching and data compression in information theory.


[1]  M. Abadi and A. Galves. Inequalities for the occurrence times of rare events in mixing processes. The state of the art. Inhomogeneous random systems (Cergy-Pontoise, 2000). Markov Process. Related Fields  (2001), no. 1, 97–112.

[2]  L. Barreira. Hyperbolicity and recurrence in dynamical systems: a survey of recent results. Resenhas  (2002), no. 3, 171–230.

[3]  A. Dembo and I. Kontoyiannis. Source coding, large deviations, and approximate pattern matching. Special issue on Shannon theory: perspective, trends, and applications. IEEE Trans. Inform. Theory  (2002), no. 6, 1590–1615.

[4]  G. Reinert, S. Schbath, and M.S. Waterman. Probabilistic and Statistical Properties of Finite Words in Finite Sequences. In: Lothaire: Applied Combinatorics on Words, Cambridge University Press, J. Berstel, D. Perrin, eds. (2005).

[5]  P.C. Shields. The ergodic theory of discrete sample paths. Graduate Studies in Mathematics . American Mathematical Society, Providence, RI, 1996.



David Coupier, Laboratoire Paul Painlevé & Université Lille 1
Tomasz Downarowicz, Institute of Mathematics Computer Science, Wroclaw University of Technology
Jorge Freitas, Universidade do Porto
Stefano Galatolo, Dipartimento di matematica applicata "U. Dini
Marc Kesseböhmer, Universität Bremen
Ioannis Kontoyiannis, Athens University of Economics & Business
Yves Lacroix, Centre de Physique Théorique
Jérôme Rousseau, CNRS & Université de Bretagne Occidentale
Benoît Saussol, CNRS & Université de Bretagne Occidentale
Sophie Schbath, Institut National de la Recherche Agrononique
Sandro Vaienti, Centre de Physique théorique, Luminy
Nicolas Vergne, CNRS - Université d'Evry
Benjamin Weiss, The Hebrew University of Jerusalem
Roland Zweimüller, University of Vienna


There will be three minicourses of 3 hours each, by Benoît Saussol (ergodic theory), Sophie Schbath (mathematical biology), and Ioannis Kontoyiannis (information theory).

Monday - Tuesday - Wednesday - Thurday - Friday

Monday November 3, 2008

10.00-10.30 Opening and introduction  


B. Saussol 1/3

An introduction to quantitative Poincaré recurrence in Dynamical Systems

11.00-11.30 Break


B. Saussol 2/3

An introduction to quantitative Poincaré recurrence in Dynamical Systems

12.30-13.30 Lunch


J. Rousseau

Poincaré recurrence for observations

14.30-14.45 Break


Y. Lacroix

On the law of series in ergodic theory

Tuesday November 4, 2008

10.00-11.00 S. Schbath 1/3 The statistical world of motif occurences along DNA sequences

11.00-11.30 Break


S. Schbath 2/3

The statistical world of motif occurences along DNA sequences

12.30-13.30 Lunch


M. Kesseböhmer

Distorted critical return time processes and continued fraction

14.30-14.45 Break


N. Vergne

Poisson approximation for search of rare words in DNA sequences
18.00 Conference dinner in Braziliaans eetcafé Carioca -  Grote Berg 4, Eindhoven (040-2455337)

Wednesday November 5, 2008

10.00-11.00 S. Schbath 3/3 The statistical world of motif occurences along DNA sequences

11.00-11.30 Break


B. Saussol 3/3

An introduction to quantitative Poincaré recurrence in Dynamical Systems

12.30-13.30 Lunch


B. Weiss

Recurrence in random fields - a survey

14.30-14.45 Break


S. Vaienti

The Rényi entropy function and the large deviation of short return times

15.45-16.00 Break


S. Galatolo

Shrinking targets, decay of correlations and arithmetical properties

Thursday November 6, 2008

10.00-11.00 I. Kontoyiannis 1/3 Pattern matching for data compression and sequence analysis

11.00-11.30 Break


I. Kontoyiannis 2/3

Pattern matching for data compression and sequence analysis

12.30-13.30 Lunch


D. Coupier

Local configurations in the Ising model

14.30-14.45 Break


T. Downarowicz

The "law of series" in typical processes

15.45-16.00 Break


J. Freitas

The link between Hitting Time Statistics and Extreme Value Theory

Friday November 7, 2008

10.00-11.00 I. Kontoyiannis 3/3 Pattern matching for data compression and sequence analysis

11.00-11.30 Break


R. Zweimüller

Return times and hitting times in infinite ergodic theory

12.30-13.30 Lunch

Practical Information


There is no registration fee.



Conference Location and Travel

The workshop location is EURANDOM,  Den Dolech 2, 5612 AZ Eindhoven, Laplace Building, 1st floor, LG 1.105.

EURANDOM is located on the campus of Eindhoven University of Technology, in the 'Laplacegebouw' building' (LG on the map). The university is located at 10 minutes walking distance from Eindhoven railway station (take the exit north side and walk towards the tall building on the right with the sign TU/e).

For information on how to come to Eindhoven, please check


EURANDOM made a preliminary group reservation in

- Sandton Hotel Eindhoven City, Stratumsedijk 23d/f, Eindhoven. Special price single room  87* euro, double room 97* euro (breakfast included).

- Hotel Queen, Markt 7, Eindhoven, 040-2452480, Special price single room 92,50*,  double room 112,50* euro (breakfast included).

 * excl. tourist tax 3,50 euro per night.

If you want EURANDOM to make a reservation, indicate the requested nights on the registration page.

For private bookings we suggest you consult the web pages of the Tourist Information Eindhoven, Postbus 7, 5600 AA Eindhoven.


November 3-7, 2008 lunches are being organised; these are free of costs for all participants, if ordered on the registration form.

On  November 4, there will be a conference dinner. For non-invitees an amount of 35 euro is requested, to be paid at arrival in cash (preferably exact amount in euros). Indicate your attendance on the registration form.


For more information,  please contact Mrs. Lucienne Coolen, workshop officer of  EURANDOM, at coolen 'at'


Jean-René Chazottes, CNRS / École Polytechnique (jeanrene'at'
Frank den Hollander, Universiteit Leiden (denholla'at'
Frank Redig, Mathematisch Instituut Universiteit Leiden (redig'at'

The Organizers would like to acknowledge the following organizations for their contributions



Last modified: 24-02-09
Maintained by
Lucienne Coolen