*Journées de Probabilités 2007*

**Semen Shlosman **

*Coherence Phase Transition in the Information Networks *

I will describe the phenomenon of the phase transition, which takes place in large networks, as one increases the number of clients per server. The transition results in the slowing down of the rate of convergence to the stationary state. At low load it does not depend on the the size of the system, while at high load it grows with the size of the network.

In the corresponding infinite network the parameter of the load per node plays the role similar to that of the temperature in statistical mechanics. At high load the large network can enter into coherent state, with different nodes evolving in a synchronous manner, keeping the same "phase".

I will expain the concept of the non-linear Markov process, which arises naturally in this context.