Jeudi 10 février 2005
The discrete microscopic structure of macroscopic objects was postulated at the time of Democritus. The crucial relevance of this became evident in modern times, starting with Dalton’s laws in chemistry, and culminated in physics with the statistical mechanics of Boltzmann and Maxwell.
It turns out that in most biological and social systems, and more generally in systems with auto-catalytic interactions (proliferation, contagion, information spread), the discreteness of the elementary components and interactions (e.g. giving birth to a new individual, informing a neighbor of a new product, adoption of a new idea by an individual, contracting a disease) is even more crucial.
Indeed, in many cases, the continuum approximation predicts a uniform, static (life-less) asymptotic state. In reality such systems present generically
emergent spatio-temporal localized objects with unexpected collective dynamical properties : adaptability, resilience and sustainability.
I will present the generic mechanism in terms of the renormalization group, some recent mathematical proofs based on branching random walks and applications to real phenomena.