# Colloquium Talk - Stefano Luzzatto (ICTP): Determinism and Randomness from a Dynamical Systems viewpoint

**Abstract**: Determinism and Randomness are often thought of as opposites, and equated with Predictability and Unpredictability respectively, but in fact the relationships between these concepts are much more subtle than they initially appear. Most (if not all) physical phenomena are deterministic, in the sense that their behaviour is a direct consequence of physical laws, but not all are predictable and some, even simple processes such a flipping a coin, are often referred to as random (indeed flipping a coin is used to as the archetypical random process in most introductory probability textbooks).

In this talk I will try to “disentangle” these apparent contradictions using some examples of Dynamical Systems which illustrate in a very simple setting how a deterministic system can have unpredictable “chaotic” behaviour and when we can think of it as having some features which justify referring to it as “random” and what exactly we mean by this. In particular, this involves distinguishing between short term unpredictability and long term statistical predictability, which is formalised mathematically through the notion of “Physical Measure”.

Most of the talk will be completely introductory, in the second part I will mention some open research questions.