## Section: New Results

### Statistical models for corpus linguistics

Participants : Olivier Catoni, Thomas Mainguy.

In [21] we describe a language model as the invariant measure of a Markov chain on sentence samples. The kernel of this Markov chain is defined with the help of some context free grammars : from the sentence sample, a random parse model produces a context free grammar with weighted rules, and from this grammar, a new sentence sample is formed by applying the rules randomly. We prove various mathematical properties of this Markov process, related to its computation cost and the fact that it is weakly reversible and therefore ergodic on each of its communicating classes. As a companion to the Markov chain on sentence samples, we can also define a Markov chain on weighted context free grammars. This leads to another type of grammar, that we called Toric Grammars, defined by a family of context tree grammars that can be computed from any of its members as the communicating class of a Markov chain on context free grammars with weighted rules. Preliminary simulations on small data sets are very encouraging, in that they show that this type of model is able to grasp the recursive nature of natural languages.