Professor Roberto Fernández
 Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS, Université de Rouen.


SEPTEMBER 26, 2007
EURANDOM, Laplace Building TU/e, Green Lecture Room (LG 1.105)


* For organizational reasons please send an e-mail to if you plan to attend.

15.15 Coffee/Tea



Welcome by Professor Onno Boxma, Scientific Director EURANDOM

Professor Kees van Hee, Dean of the Department of Mathematics and Computer Science TU/e
Professor W.Th.F. den Hollander, Leiden University and EURANDOM











Random processes, partially ordered fields, gibbs fields

These probabilistic objects are all defined in terms of families of probability kernels satisfying appropriate consistency relations.
This common feature can be exploited to develop parallel theories in which concepts and techniques can be shared or imported. The talk will (i) present the main lines of this parallel treatment; (ii) discuss the resulting body of comparable properties (extremality and mixing, limit states, Dobrushin uniqueness criteria); (iii) review instances of interplay between the theories (phase transitions, uniqueness criteria), and (iv) present some remaining questions and open problems.

Short Biography of Roberto Fernández

Roberto Fernández is professor of mathematics at the university of Rouen in France since 1999.
Before he moved to Rouen, he held positions in Lausanne, Zürich, São Paulo, Princeton and several other universities in the US. He received his basic academic training in his native country, Argentinia.

Roberto's research interests lie at the interface between probability theory and statistical physics.
He has made major contributions to both fields, in particular, to the area of Markov chains (speed of convergence to equilibrium, perfect simulation,metastability) and to the area of Gibbs theory (classical and quantum critical phenomena, renormalization, stochastic dynamics). He is the author of a monograph, written jointly with J. Fröhlich and A. Sokal, on critical phenomena in classical and quantum statistical physics.

16.30 h. Reception



Professor Roberto Fernández
 Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS, Université de Rouen.


Dates: Tuesday October 2, 16, 23 and 30, 2007
Time: 10.30-12.30 h.
Place: EURANDOM, Laplace Building, LG 1.105
* Please send an e-mail to if you plan to attend.

Fields and Processes: common framework and relations

The course will present a common framework yielding general properties of lattice fields and discrete-time processes. This framework is based on the notion of consistency: consistency with finite-volume conditional probabilities defines a lattice field, while consistency with transition probabilities defines a discrete-time process. The attributes of the constraining probability kernels in each of these cases lead to the notion of oriented specification. Much of the general theory follows from the probabilistic properties of these oriented kernels. The theory accommodates also the so-called partially ordered fields, originally introduced for image reconstruction, whose features are in many senses intermediate between those of processes and (unordered) fields.

Tentative program:

1) Basic definitions, oriented specifications, examples, reconstruction from single-site kernels.

2) Extremality, tail-field triviality, mixing properties, limit measures. Translation invariance and ergodicity.

3) Overview of uniqueness results (boundary uniformity, Dobrushin criterion, disagreement percolation) and examples of phase transitions.

4) Relation between processes and one-dimensional fields. Phase transitions in the half line.

Last modified: 23-02-09
Maintained by L. Coolen