to be held, from 21 to 25 October 2013, at CIRM, in Luminy (Marseille).
The school will present, in particular, three series of two lessons,
five invited seminars, plus a few short seminars.
 !!! INFORMATION TO PARTICIPANTS AT THE BOTTOM OF THE PAGE !!! 
The lectures are:

Patrik Ferrari
Markov chain dynamics and interpretations in random tiling,
particle systems and random matrices
We will first explain the construction of a dynamic on Markov chains,
which preserves a nice class of measures on interlacing particles
configurations. Such systems arises in some random tiling models (for
instance in the Aztec diamond), in interacting particle systems
systems, and have connections to random matrices too. We will then
apply the construction to some examples to see how it works in a
concrete situation.
What kind of results can be obtained in the limit of large time t?
To the particle system we initially considered one could associate
also a height function. In the large time limit, the height profile
presents some facets and a disordered region, the bulk. The
fluctuations in the bulk are Gaussian in the (ln(t))^(1/2) scale (it
is a Gaussian Free Field), while at the edge of the facets the
fluctuations live on the t^(1/3) scale and are governed by the
TracyWidom distribution first discovered in the context of random
matrices.


Jan Swart
Duality and intertwining of Markov Processes
Markov process duality is a very strong tool in Markov process theory
with applications, e.g., in the theory of diffusions and in the field
of interacting particle systems. In the latter, in particular, many of
the elementary models have useful duals and have been much studied
partly just because of that.
In my first lecture, I will address the question how to systematically
look for dualities, treating the LloydSudbury theory for
nearestneighbour systems and giving examples.
In my second lecture, I will look at the related but less wellknown
concept of intertwining of Markov processes and treat special
examples, such as the lookdown construction of the WrightFisher
diffusion and trimmed trees of branching processes, in a unified
framework.


Remco Van der Hofstad
The smallworld nature of Random Graphs
Empirical findings have shown that many realworld networks share
fascinating features. Indeed, many realworld networks are small
worlds, in the sense that typical distances are much smaller than the
size of the network. Further, many realworld networks are scalefree
in the sense that there is a high variability in the number of
connections of the elements of the networks. Therefore, such networks
are highly inhomogeneous. Spurred by these empirical findings, models
have been proposed for such networks.
In this course, we discuss empirical findings of realworld networks,
and describe some of the random graph models proposed for them. We
then discuss the smallworld phenomenon in random graphsand its link
to `six degrees of separation'. We further discuss flows on random
graphs, where the edges are equipped with general independent and
identically distributed edge weights. We highlight some of the
ingredients used in the proofs, namely the treelike nature of the
random graphs under consideration and the use of branching processes.
The first lecture will mainly deal with realworld networks and random
graphs, while the second one will deal with the smallworld phenomenon
in weighted and unweighted random graphs.

A tentative program
is here.
Note that the school will be over at 16.30 on Friday 25th, so
you may plan a trip back on Friday evening.
The registrations are now opened!
Please try to register before the end of August! This is done through
the CIRM portal.
(the registration link at the CIRM portal
should look like this).
The procedure is in two (simple) steps:

you register for the inscription;

your inscription will be then validated by the organisers, who will
notify this to you by email.
sorry about this complicancy, but that's for compliance with CIRM rules.
We hope to have many of you here!
The organisers,
Frédérique Bassino,
Brigitte Chauvin,
Michèle Soria,
and the scientific committee of ALEA in Europe.
For those of you who do not know what
CIRM
is...
The CIRM, Centre International de Rencontres Mathématiques, is
a wonderful institution, hosted within the
Luminy scientific campus of the AixMarseille University, that,
among other things, provides a congress center with cosy inplace
housing facilities, and comfortable common spaces for scientific
research, and leisures (including a rich library). It is at walking
distance to the natural landscape of calanques, i.e. white
cliffs over the Mediterranean surrounded by the typical local
vegetation.
Coming to CIRM is moderately easy. You find some informations on the
CIRM webpage.
(Here, a photo of the calanques)
Information to participants
The program is planned to start on Monday morning, 21st,
and end at 16.30 of Friday 25th. For this reason, for
participants whose lodging is supported by the school, the night
20>21 is payed, but the night 25>26 is not (although it is
possible to stay one more night at CIRM, if you need it).
The `normal' plan is to arrive on 20th, Sunday afternoon (but
recall that CIRM opens only at 16h30 ???? CHECK THIS ?????. A
light dinner will be served on that evening, also for you, if you
check the appropriate box in the inscription form!). Then, if
compatible with the length and times of your travel back, we shall
leave in the afternoon of the 25th, Friday. Consider at least
40min, by bus and then subway, to Marseille downtown and main
train station.
For those of you going back to Paris, or through Paris, by train
TGV, the trip takes around 3h15, and trains leave from Marseille gare
St. Jean at
17h36, 18h08, 18h36, 19h36, 20h08,... so it shall be doable
with no much trouble.
All remarks for the webmaster: Andrea Sportiello
andrea.sportiello at lipn.fr
