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:
Markov chain dynamics and interpretations in random tiling, particle systems and random matricesWe 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 Tracy-Widom distribution first discovered in the context of random matrices.
Duality and intertwining of Markov ProcessesMarkov 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 Lloyd-Sudbury theory for nearest-neighbour systems and giving examples.
In my second lecture, I will look at the related but less well-known concept of intertwining of Markov processes and treat special examples, such as the look-down construction of the Wright-Fisher diffusion and trimmed trees of branching processes, in a unified framework.
Remco Van der Hofstad
The small-world nature of Random GraphsEmpirical findings have shown that many real-world networks share fascinating features. Indeed, many real-world networks are small worlds, in the sense that typical distances are much smaller than the size of the network. Further, many real-world networks are scale-free 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 real-world networks, and describe some of the random graph models proposed for them. We then discuss the small-world 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 tree-like nature of the random graphs under consideration and the use of branching processes.
The first lecture will mainly deal with real-world networks and random graphs, while the second one will deal with the small-world 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 e-mail.
sorry about this complicancy, but that's for compliance with CIRM rules.
We hope to have many of you here!
and the scientific committee of ALEA in Europe.
For those of you who do not know what CIRM
The CIRM, Centre International de Rencontres Mathématiques, is a wonderful institution, hosted within the Luminy scientific campus of the Aix-Marseille University
, that, among other things, provides a congress center with cosy in-place 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