Context Free Evolution of Words

Projet MEVALRandom grammars were introduced in computer science, but the study of their thermodynamic and long time behaviour started only recently. In this paper we undertake more detailed study of context free grammars in the supercritical case, that is when the word grows exponentially fast. We study and calculate the statistics of factors for large t, prove the existence of various limiting measures and study relations between them

Spontaneous Resonances and the Coherent States of the Queuing Networks

We present an example of a highly connected closed network of servers, where the time correlations do not go to zero in the infinite volume limit. This phenomenon is similar to the continuous symmetry breaking at low temperatures in statistical mechanics. The role of the inverse temperature is played by the average load.Comment: 3 figures added, small correction