Large Deviations Theory for Chemical Reaction Networks (Andrea Agazzi, Geneva University, Switzerland)

22.05.2017 15:15 – 17:15

At the microscopic level, the dynamics of networks of chemical reactions can be modeled as jump Markov processes whose sample paths converge, in the limit of large number of molecules, to the solutions of a set of algebraic ordinary differential equations. Fluctuations around these asymptotic trajectories can in principle be studied through large deviations theory in path space, also called Wentzell-Freidlin (W-F) theory.
However, the specific form of the jump rates for this family of processes does not satisfy the standard regularity assumptions imposed by that theory, and weaker conditions need to be developed to deal with the framework at hand. In this talk, I will first review the class of models under investigation and some relevant theorems from W-F theory. Using tools of Lyapunov stability theory I will then design sufficient conditions for the applicability of large deviations estimates to our class of Markov processes. Translating these conditions in terms of the topological structure of the chemical reaction network, I will finally define a large class of chemical reaction systems to which such estimates can automatically be applied, and conclude by outlining some of the proofs in the process above.

This is joint work with Amir Dembo and Jean-Pierre Eckmann.

Lieu

Room 17 15:15-16:00 & Room 17 16:30-17:15, Séminaire "Mathématique Physique"

Organisé par

Section de mathématiques

Intervenant-e-s

Andrea Agazzi, Geneva University, Switzerland

entrée libre

Classement

Catégorie: Séminaire