10:45
11:45

For each integer K, we define SK as the set of paths of length K and step +1 or -1 in ZK. The random walk of the K prisoners is a random walk on this set SK . Emmanuel Boissard, Serge Cohen, Thibault Espinasse and James Norris have shown that the trajectories of the first prisoner behave globally like simple random walks with variance inversely proportional to the length K of the chain. The challenge is to understand what happens when K tends to infinity: the limit behaviour of the first prisoner is "subdiffusive", but we don't know how to quantify this assertion.
We will see how we can define a natural limit process. In particular, we will show how calculating its transition probability gives rise to continued fractions.
This family of processes can be seen as a family of random walks on the configuration graph of the (square(e)) ice model (or 6-vertex model). We will finish by explaining how to make the link in order to exploit this connection.
(Joint work with Serge Cohen, IMT/UT3)

Salle 76